Fast Paced Multiplayer Interpolation/Extrapolation or both?

Hey guys i have a few questions for the more experienced users among you.
When doing a fast paced game like an action rpg or something like a 2D action shooter how you handle the latency issue?
The problem with extrapolation is, that it can predict wrong positions expacially when the player changes direction very quickly. So in result the correction can look a little weird and the higher the latency is the more incorrect the results are.
In interpolating things i see the problem, that the clients are noch perfectly in sync and something like traps , moving walls, which crash the player and so on ,are a problem because one client might see the player running into a trap while the other player with lower latency saw him dodging it. I know this is often discussed but how do expert game programmers handle it ?.
Are they only interpolating and do some extrapolation with hunge lag and take the different player views as they are or is there something else you can do about it to at least give the player the illusion that things are in sync?