US President Barack Obama has said the UN climate conference in Paris could be a "turning point" in global efforts to limit future temperature rises.
Negotiators from 195 countries will try to reach a deal within two weeks aimed at reducing global carbon emissions and limiting global warming to 2C (3.6F).
Leaders from 147 nations have been addressing the meeting, known as COP21.
President Obama urged negotiators to deliver a meaningful deal, because the "next generation is watching".
He told delegates: "Climate change could define the contours of this century more than any other (challenge).
"I came here personally to say the United States not only recognises the problem but is committed to do something about it."
He added that recent years had shown that the global economy had grown while emissions had remained flat, breaking the old arguments for inaction "that economic growth and environmental protection were in conflict".
Russian President Vladimir Putin also addressed the conference.
During negotiations for the preceding Kyoto Protocol, Russia was the last industrialised nation to ratify the global agreement, allowing the landmark deal to come into force in 2001.
Echoing President Obama, Mr Putin said: "We have demonstrated we can ensure economic development and take care of our environment at the same time."
In a diplomatic play on semantics, probably to highlight the differing points of view between industrialised and emerging economies, Chinese President Xi Jinping told the conference he did not see the Paris talks as a turning point nor a "finish line, but a new starting point".
He said that climate change went beyond national borders and that it was "a shared mission for all mankind", before reiterating China's pledge to start cutting its emissions from a peak in 2030.
Analysis - Matt McGrath, BBC environment correspondent, at COP21
So what can we glean from the warm words and good intentions of the leaders?
There are certainly positive omens. Leader after leader sang the same hymn - climate change is a huge challenge, only co-operation on a global level can solve it, and my country is doing great!
Still, there were obvious divisions.
Progress may or may not happen over the next two weeks.
One negotiator told me the whole idea was for the leaders to come, speak and happily be on their way without toppling this carefully constructed applecart.
Unlike in Copenhagen in 2009.
"The leaders fully understand the political nature, the political difficulties. They are coming here to provide manoeuvring guidance," he said with a hint of irony.
"And we as negotiators will then have to fix it."
British Prime Minister David Cameron used his address to consider how future generations would respond to the idea that it was "too difficult" for this generation of politicians to reach an agreement in 2015.
"Our grandchildren would ask why it was so difficult," he said, before listing how progress had been made in delivering climate policy, such as financing, carbon budgets and technological research and development.
"Instead of making excuses to our children and grandchildren, we should be taking action," Mr Cameron stated.
Tuvalu Prime Minister Enele Sopoaga made a stark observation in his passionate address: "If we save Tuvalu, we will surely save the world."
"Like other nations in the Pacific, our survival depends on the decisions we take here in Paris," he said, reflecting the concerns of many Small Island States (SISs) around the globe.
"We stand on a cliff edge. Either we stand united and agree to combat climate change, or we all stumble and fall."
Major points of contention include:
- Limits: The UN has endorsed a goal of limiting global warming to no more than 2C over pre-industrial levels by the end of the century. But more than 100 poorer countries and low-lying, small-island states are calling for a tougher goal of 1.5C.
- Fairness: Developing nations say industrialised countries should do more to cut emissions, having polluted for much longer. But rich countries insist that the burden must be shared to reach the 2C target.
- Money: One of the few firm decisions from the 2009 UN climate conference in Copenhagen was a pledge from rich economies to provide $100 billion (93 billion euros) a year in financial support for poor countries from 2020 to develop technology and build infrastructure to cut emissions. Where that money will come from and how it will be distributed has yet to be agreed.
Much of the discussion in Paris is expected to centre on an agreement to limit global warming to 2C (3.6F).
However, assessments of the more than 180 national climate action plans submitted by countries to the summit suggest that if they are implemented, the world will see a rise of nearer to 3C.
Christiana Figueres, the head of the UN's climate change negotiations, told delegates that never before had a responsibility so great been in the hands of so few.
"The world is looking to you," she said. "The world is counting on you."
The talks are taking place amid tight security, two weeks after attacks in Paris claimed by the so-called Islamic State (IS) group.
World leaders are attending the start of the two-week meeting to give impetus to the talks, after the high-profile failure of the Copenhagen summit in 2009.
UN climate conference 30 Nov - 11 Dec 2015
COP 21 - the 21st session of the Conference of the Parties - will see more than 190 nations gather in Paris to discuss a possible new global agreement on climate change, aimed at reducing greenhouse gas emissions to avoid the threat of dangerous warming due to human activities.
COP21 live: The latest updates from Paris
Explained: What is climate change?
In video: Why does the Paris conference matter?
Analysis: From BBC environment correspondent Matt McGrath
More: BBC News special report
What are the specific goals of COP21?
The ultimate aim is to limit warming to 2C (3.6F) above pre-industrial levels, widely seen as a dangerous threshold. Since 1880, the average global temperature has already risen by almost 1C. About 0.6C of this has occurred in the past three decades.
Why does this matter?
When the Earth warms about 2C above pre-industrial times, scientists say there will be dangerous and unpredictable impacts on our climate system. And we're already half-way to that danger point.