A recent news report suggests that time–reversal violation may have been observed in neutrino reactions. (You can read the paper on which the report is based here.) Why is this important? Because it may shed light on a long-standing puzzle and that is why it is that in the universe we inhabit, matter is vastly more abundant than anti-matter.
Why is this a puzzle? Because when matter is created out of pure energy, it seems to be always the case that the amount of matter and anti-matter are identical. So in the Big Bang when energy was transformed into all the matter and anti-matter now in the universe, there should have been equal numbers of both. But since we now see so little anti-matter, it has been argued that this is because of the violation of what is known as ‘time-reversal symmetry’, that causes anti-matter to decay at a different (and faster) rate than matter, leading to its current depleted quantities. [UPDATE: See a correction to this in the comments.]