You can cut back the overhang, but you must not cut back any further than your boundary (imagine the fence was 50feet tall, that's the line you're allowed to cut back to)
You must offer the cut off parts back to the neighbour, but they do not have to accept them, if they don't accept them it's your responsibility to dispose of them, you cannot just throw the cuttings over the fence (which seems to be widely believed)
But as above, for good relations it's always better to talk to the neighbour before just going ahead and doing it, but if they are problematic about it you can just go ahead and do it.