In the UK, omega-3 has been a big fad, it seems. You can't seem to get away from products without it. I Although recently it has died down, it mainly stems back to a flawed study on schoolchildren. Is there any peer reviewed and well researched evidence pointing to a conclusion either way?
And this article suggest omega-3 "might offer a new way of protecting against traumatic brain injury (TBI)"
While this study suggest that "DHA Improves Memory and Cognitive Function in Older Adults",
this one says
both studies were published in 2010.
Omega-3 has been associated with various benefits but many of the studies to measure them have been poor, hence the controversy.
The basic theory that they are important for proper brain function (a much broader idea than just concentration and cognitive ability) was, I think, best articulated in the book The Madness of Adam and Eve by David Horrobin as part of a theory about how the modern human brain developed.
The most interesting study I know of supporting this was conducted as a randomised controlled trial on prison inmates reported here (see also the news comment from the Guardian and the BBC where the prison service seem to express some doubts). But replication trials from other countries are due to report this year. So we might safely say there is some evidence that omega-3s can reduce disfunction.
But there have been badly constructed trials as well, intended to show improvements in children in school. Ben Goldacre demolishes the design of the Durham Experiment thus:
I have not found a similar demolition of the results on reducing bad behaviour in prisoners. This might be because a lack of omega-3s cause anti-social effects but, when you have an adequate diet, further omega-3s make little difference.