Conflicts can involve different nations and religions, different races and classes. Some of them seem intractable: the tensions and hatred seem depressingly permanent. But there are a number of social psychologists who have been studying how prejudice and distrust between groups can be overcome.
Eran Halperin is associate professor at the School of Psychology at the Interdisciplinary Centre, Herzliya, Israel, and has carried out many experimental studies to test how people can be encouraged to think more favourably about the "other" group, and be more willing to reach a deal.
In one experiment a group of Israelis was given a fake newspaper article. It described a Palestinian leader criticising his own society - corruption in Gaza and the West Bank or shortcomings at schools. A group of Palestinians was likewise exposed to Israelis being self-critical.
"One of the major barriers to conflict resolution is that people just won't listen to what the members of the other group are saying. We were looking for a way to make them listen that is feasible and effective.
"We used a real speech by Knesset member Ahmad Tibi, a Palestinian citizen of Israel, who talked about the Holocaust as one of the major disasters in the history of humankind, something that is incomparable to any other disaster of any other society.
"After Israelis were exposed to this speech, suddenly they were willing to be exposed to things that he or other members of the Palestinian society were saying about other issues.
"And if Israelis hear a Palestinian leader - or just a Palestinian citizen - saying something critical about the educational system, or corruption within the Palestinian government, then suddenly they are much more open to hear what Palestinians have to say about issues related to the conflict.
"We found exactly the same results when Palestinians were exposed to Israelis criticising their own group."
The effect seems to be achieved by disrupting the idea of monolithic blocs, the idea that the other group is overwhelmingly dominated by a single identity, a single value system, a single political objective.
In July this year, Iran finally signed a deal with major powers around the world to freeze its controversial nuclear programme in exchange for the lifting of international sanctions. Sanctions had been in place for years, and were hitting the Iranian economy. The puzzle, then, was why the deal had taken so long to reach.
Nick Wright of the University of Birmingham has a background in neuroscience, which he now applies to international conflict:
"Why has Iran been prepared to accept costs of some $100bn to pursue its nuclear programme?
"If you listen to what the Iranians actually say, it's that, as Foreign Minister Javad Zarif put it at the end of 2013, imagine you're told you cannot do something that everyone else can do. What would you do? Would you relent or would you stand your ground?"
Here's a thought experiment. Imagine that Fred had been given a £10 windfall and had been told he must share it with you. You can choose to accept or reject Fred's distribution. If you accept it, you get to keep what Fred offers you. But if you reject it, you both get nothing.
If Fred offers you half the money, you'll almost certainly accept: £5 to you and £5 to Fred. But what if Fred offers you only £1? After all, £1 is still better than nothing.
"If you only cared about what you were going to receive, obviously you should choose to accept the nine-one split, because you're getting £1 rather than nothing.
"But what most people do is they say, 'Oh, God, that's terribly unfair! You're getting £9 and I'm only getting £1. That's very unfair and I'm going to reject it.'
"People are prepared to forego money in the name of fairness."
And it turns out that offers of less than 25% in this type of experiment are routinely rejected. That's true whether you conduct the experiment in London or Lagos, India or Indonesia.
Almost all of us have so-called "sacred values". These aren't necessarily religious values: they're values which are core to identity, the values which drive and define us.
Anthropologist Scott Atran has written extensively about terrorism, violence and religion.
"Sacred values differ from material values precisely because all the traditional assumptions of rational actors, of utility, of trade-offs fly out the window."
If you try to bargain with sacred values it can prove disastrous:
"When things are sacred, if you try to trade them off, not only doesn't it work but it backfires. Suppose I offered you money for your child. You might think I'm crazy. If I insisted, you might get angry.
"It's the same for people who offer to trade money for your being a traitor to your country or your religion, or for the right of return or for whatever sacred value you may hold.
"In experiments, the more material incentives are offered, the greater the insult, and the more violent people get in the defence of those values.
"I briefed the United States Military Command for the Middle East, and people would sort of understand what I was talking about, and believe that they themselves have sacred values which they're defending.
"But the difficulty is getting them to believe the others are also operating on the basis of sacred values. People tend to conceive of their enemies as strict consequentialists - simply out for the short-term gain of power - or that they're crazy or nihilists.
"That is a great mistake, because the force of intractable and enduring conflict comes from a clash over sacred values more than it does over material interests."
In parts of Northern Ireland, the two main communities, Protestant and Catholic, have virtually no contact with each other. What contact they do have is often hostile: for example, during the summer marching season. But whether the walls are in West Belfast or the West Bank, lack of interaction can make one side blind to the humanity of the other.
Prof Miles Hewstone is the director of the Oxford Centre for the Study of Intergroup Conflict, part of Oxford University, and is a leading proponent of contact theory.
"Contact theory is the idea that you can reduce prejudice by members of different groups by bringing them together under positive conditions."
Five years ago two schools in Oldham, one of Britain's most racially segregated towns, were merged to create Waterhead Academy. It was a good test:
"They took two pre-existing schools, Breeze Hill and Counthill, one of which was almost entirely white British, the other was almost entirely Asian British, and said, 'We'll take this pint of milk, we'll take this pint of Guinness and we'll pour them into a new quart pot.'
"What is interesting is that the data are going the way we would have hoped - slowly but gradually. There is an indication that the social networks of the Asian students and the white British students are becoming more mixed.
"Within just three months we've got more gender links and are beginning to break down some of the racial isolation."
Although the effect is not dramatic, the school merger does seem to have improved relations.
Contact theory, self-criticism, understanding sacred values and perceptions of fairness: these are no panacea for settling conflict, but they do offer a greater insight into what motivates enmity, and so how it might be diminished and overcome.
They could be psychologically useful levers in the pursuit of peace.
Such theories advocate a different approach in the attempt to bring warring parties together. But they raise the question: do we have the courage to embrace this unconventional approach and the possibilities it presents?