The day began at 08.00 GMT with a statement from Parliament President Martin Schulz on the 70th anniversary of the liberation of the Auschwitz concentration camp.
MEPs were then joined by Italian Prime Minister Matteo Renzi to review the county's six-month presidency of the Council of Ministers, which came to an end this month (see 'Key Video').
After that, MEPs debated and approved a compromise on new EU legislation which aims to give member states greater powers to ban the cultivation of genetically-modified (GM) crops on their territory.
The afternoon session opened with a debate with Donald Tusk, the new head of the European Council, on the results of last month's summit of EU leaders.
After that, there were debates on the situation in Libya, illegal migration into the EU via the Mediterranean, and possible EU laws to set a quota for women on company boards.
Business closed with statements from the Commission and the Council of Ministers on EU-wide efforts to tackle organised crime, and the alleged surveillance of lawyers in some member states.
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By Paul Seddon
All times stated are UK
End of Session
And with that, this evening's session is finished.
The plenary sitting will resume at 08.00 GMT tomorrow, when MEPs will be joined by the Latvian Prime Minister Laimdota Straujuma to discuss the priorities of Latvia's six-month presidency of the Council of Ministers, which began on 1 January this year.
Time for investigation
German Green MEP Jan Philipp Albrecht, the final scheduled speaker in this short debate, says that it is "high time" that the Commission investigates cases of inappropriate surveillance and pushes for a clearer definition of what exactly constitutes "national security".
We'll now have five minutes of "catch the eye", during which speakers not on the list can make short interventions by getting the attention of French MEP Sylvie Guillaume, who is chairing this debate.
Justice commissioner Vera Jourova opens the debate by telling MEPs that the EU's Charter of Fundamental Rights, which includes rules on client-lawyer secrecy, does not apply to national authorities when they are carrying out surveillance for national security reasons.
The debate has been requested by Dutch MEP Judith Sargentini, on behalf of the Parliament's Green group. It follows an allegation in the Dutch press that an American law firm in Amsterdam has been put under surveillance by the Dutch security services.
Lawyer surveillance debate
That's the debate on organised crime and corruption finished.
Finally this evening, MEPs are going to be debating the alleged state surveillance of lawyers in the EU, with statements from the European Commission and Council of Ministers.
Eurobarometer survey published in February this year found that three-quarters of respondents thought corruption was either "fairly" or "very" widespread in their own country.
The countries where respondents were most likely to think corruption was widespread are Greece (99%) and Italy (97%).
The Nordic countries were the only Member States where a majority said they thought corruption was "fairly" or "very" rare: Denmark (75%), Finland (64%) and Sweden (54%).
As home affairs commissioner Dimitris Avramopoulos tells the chamber, the second report on the subject is due to be published in 2016.
On behalf of the Council of Ministers, Latvian Parliamentary State Secretary for EU Affairs Zanda Kalniņa-Lukaševica opens the debate by telling the chamber that Europol estimated in 2013 that 3,600 crime groups are currently active across the EU.
Organised crime debate
That's the debate on women on boards finished.
The next item on the agenda is a debate on measures that are being taken to fight against organised crime and corruption in the EU.
Italian Socialist Sergio Gaetano Cofferati - only the second man to speak during this evening's debate - says that the blockage on this legislation is "shameful" and "purely a question of ideology".
He adds that the Council, in not reaching agreement on the proposals, has effectively allowed an environment in which gender discrimination, and the denial of basic rights, has been allowed to persist.
Women on boards
Female representation on boards was highest in Finland, at 29%. It was lowest in Malta - where it was 2.8%.
The figure for the UK was 18.5%, which was slightly higher than the overall EU average.
Progress 'too slow'
Catherine Bearder - the only Lib Dem MEP in the chamber after last May's Parliament elections - says she regrets the fact that progress on the legislation has been stalled.
The adds that although the proportion of women on boards has increased in recent years, this rate of increase has been "far too slow".
Women on boards
The European Commission
published a report last October that showed that women made up only 16.6% of the boards of major publicly-listed companies in the EU.
This was a slight increase from the 2012 percentage, which was 15.8%.
The new rules would apply to all listed companies, to reflect their "economic and social responsibilities and their economic importance".
However, MEPs agreed with the Commission's proposals that the new regulations should not apply to companies that employ fewer than 250 people.
It is proposed that the law will be a temporary measure, expiring in 2028.
Women directors debate
That's the debate on smuggling incidents finished.
MEPs are now debating a proposed EU directive that would set a quota for the number of women non-executive directors on listed company boards.
The new rules, which the European Parliament agreed last November, would mean companies would have to have at least 40% female representation on boards by the year 2020, or 2018 in the case of public companies.
If they do not achieve this target, the law proposes that member states will have to dish out appropriate sanctions.
Before they could come into force, however, the proposals still need to go through the EU Council of Ministers, made up of the national ministers of the 28 member states, which could involve a lengthy negotiation.
Migration debate closes
Closing the debate on migration on behalf of the European Commission. migration commissioner Dimitris Avramopoulos tells MEPs that the Commission remains committed to taking more effective steps to tackle people smuggling, despite the fact that the smugglers have made the situation more difficult by adopting new tactics.
He says a solution to the problem will not be found without engaging the Mediterranean countries themselves, including Turkey, and finding a "co-ordinated response" amongst all EU members.
Italian MEP Salvatore Domenico Pogliese says the problem of illegal migration has become more complex since the smugglers started using the tactic of "ghost ships" to get migrants into Europe.
The tactic involves people smugglers sailing cargo ships towards Italy, and then abandon them near the coast, before the coastguard then picks them up.
Target the smugglers
Swedish centre-right MEP Anna Maria Corazza Bildt says that measures to tackle illegal migration "should target the smugglers, never the migrants".
She recommends instead that the EU work to put stronger protection of its external borders, that more countries agree to participate in search-and-rescue operations, and that more money is given to Frontex, the EU's border policing agency.
At the last plenary session, MEPs called on member states to take action against smuggling, in a resolution that said EU countries should lay down strong criminal sanctions against smuggling.
They also called for an analysis of how home affairs funds are spent, including on action to fight smuggling - and for awareness-raising campaigns on the risks posed by trying to enter the EU in such a manner.
There has been a large increase in the number of migrants trying to enter Europe via the Mediterranean over the course of the last year, mainly down to the continuing humanitarian crisis in Syria and the spread of Islamic State (IS) militants.
Last October, the
UN's refugee agency said that more than 165,000 irregular migrants had tried to cross the Mediterranean to Europe in the previous nine months, compared with around 60,000 for the whole of 2013.
The UNHCR also said that more than 3,000 died or went missing at sea, compared with just over 600 in 2013.
Maltese centre-right MEP Roberta Metsola says it is not fair or realistic for the "burden" of policing the Mediterranean to be shouldered only by those countries that border the Mediterranean.
"This is European problem that requires a European approach," she adds.
What is Mare Nostrum?
"Mare Nostrum", mentioned by several MEPs in the debate so far, is an Italian sea rescue operation for migrants that came to an end last November.
A new operation co-ordinated by Frontex, the EU borders agency, has now come into effect in the region. 21 member states have agreed to participate in it.
The new operation, however, will
only have around a third of the budget of the rescue scheme led by the Italian government, and will have a more limited scope - with coastal patrols prioritised over search-and-rescue missions.
Earlier this month, around 359 illegal migrants were rescued in the Mediterranean after the cargo ship they were travelling on, the Ezadeen, was abandoned by its crew off the coast of Italy.
The rescue came shortly after another boat carrying 796 migrants across the sea, the Blue Sky M, was abandoned by its crew near the southern coast of Italy.
Socialist leader and Italian MEP Gianni Pittella urges his colleagues to recognise that people smuggling across the Mediterranean is "one of the biggest challenges in our recent history".
He says they must consider themselves "hypocrites" unless they work effectively for a stronger EU border control policy.
Migration commissioner Dimitris Avramopoulos opens the debate by telling MEPs that the EU "cannot allow smugglers to make a fortune" from the desire of people in North Africa to make their way into Europe.
Police in Italy say they believe traffickers made some €2.5m from the migrants onboard the Ezadeen, with the passengers paying smugglers between $4,000 and $8,000 to board the ship.
Latvian Parliamentary State Secretary for EU Affairs, Zanda Kalniņa-Lukaševica, opens the debate on migration on behalf of the Council of Ministers.
This is the first time a Latvian representative has spoken to the Parliament since the country took over the rotating presidency of the Council at the start of this month.
Human trafficking cases
That's the debate on the situation in Libya finished.
The next item on the agenda is a debate following statements from the European Commission and the Council of Ministers about recent human trafficking cases in the Mediterranean.
Ms Mogherini closes the debate by telling MEPs that she feels Libya may even be "beyond" being a failed state.
She adds that the country has a high concentration of arms, large migrant flows across the country's borders, and high levels of religious radicalisation, meaning they should all be "extremely worried" about any worsening of the violence in the country.
In response to MEPs who criticised EU involvement in the region, she rejects the idea of the Union deliberately taking a back seat, telling the chamber that "we can stay away from Libya, but Libya will not stay away from us".
Nevertheless, she tells MEPs that she would like to see the bloc's foreign policy role in the country "better defined" after the talks in Geneva have finished.
MEPs will vote on a resolution on the matter on Thursday.
Last week, Turkish Airlines - the last foreign airline operating in the country -
It followed an EU ban on all Libyan airlines from flying over the bloc's airspace because of aircraft safety concerns.
That's the end of the scheduled speeches for this debate. MEPs who were not on the list to speak now have the chance to do so, during the five-minute 'catch the eye' procedure.
These short free-for-alls contrast with the regimented bulk of the Parliament's debates, when speakers representing each political grouping take part according to pre-arranged lists.
After the unscheduled speeches, Ms Mogherini will wind up the debate on behalf of the Commission.
Slovakian MEP Branislav Škripek highlights the plight of Christian groups in Libya, whom he says have become the "biggest victims" of the violence sweeping the country.
Western intervention criticised
French Front National MEP Louis Aliot tells Ms Modgerini that the EU should not seek to intervene in the peace negotiations, instead leaving the Arab League to take control of the negotiations.
He says he sees the current crisis in Libya as a consequence of Western intervention, and criticises what he calls the "incredible arrogance" of European nations, who he says intervened in the country's affairs believing "they could run the world".
Libya's recent history
Col Muammar Gaddafi's 42-year rule came to an end in 2011, when - after months of stalemate and a Nato-backed series of airstrikes - rebels stormed the capital Tripoli in August.
A transitional government took charge, before elections to establish a General National Congress - the country's first free national polls in 60 years - were held in July of 2012.
The body that replaced this body - the "Constituent Assembly" - came into being after elections in February last year. It has been charged with drawing up a constitution for the country, but that has been stymied by continued infighting and violence.
Spanish centre-right MEP Fernando Maura Barandiaran says he worries that failure to reach a political solution in Libya "will create the breeding ground" for terrorist groups such as Al-Qaeda and IS.
Government in Tobruk
An internationally-recognised government is based in Tobruk, near the Egyptian border, having been expelled from the capital, Tripoli, by militias last year.
However, numerous militias are in control of their own patches of territory, with successive governments struggling to exercise any kind of political control in the country.
A rival militia-backed administration now controls the capital Tripoli, while Benghazi is largely in the hands of Islamist fighters.
Country 'nearly a failed state'
Romanain Socialist MEP Victor Bostinaru tells the hemicycle that Libya is "close to a failed state", and that more must be done to ensure that Islamic State (IS) militants - which he says are already present in the country - must not be allowed to "take root".
Violence in Libya
Ms Mogherini tells MEPs that talks tomorrow in Geneva between Libya's factions - led by the United Nations (UN) - to attempt to end the conflict destabilizing country may well be the "last chance" to secure peace in the near future.
She also tells the chamber she has also added the issue of Libya to the next agenda of the next meeting of EU foreign affairs ministers.
The North African country has been plagued by factional infighting and instability since the Western-backed toppling of Colonel Muammar Gaddafi in 2011, and violence has been steadily increasing in recent months.
That's the debate on last month's EU leaders' summit finished.
We now move on to the next debate, led by EU foreign affairs chief Federica Mogerhini, on the situation in Libya.
A warm welcome?
Mr Tusk closes the debate by thanking MEPs for his welcome in his new role, noting - perhaps due to the mixed reception from some corners of the hemicycle - that he had "heard a lot about your temperament in this chamber".
Responding to Guy Verhofstadt's comments on the sharing of intelligence data, he says he hopes an agreement on the subject can be reached at next February's meeting of EU leaders.
Swift agreement hoped for
On behalf of the Commission, Foreign Affairs Chief Federica Mogherini - who is also Vice-President of the Commission - tells MEPs that the Commission, which is also meeting in Strasbourg today, has announced legislative measures to implement the proposed package of investment, and says she hopes a swift agreement on the proposals can be found with MEPs to allow investment to be released in June.