From experience with Leap alone, it appears that there are two restrictions on movement abilities.
1) You cannot leap across/over areas that are shown on the map as impassible. This is terrain you would not normally be able to walk across like the trees in the areas outside Tristram or gaps in the various dungeons. You can leap from different levels in dungeons provided those areas are adjacent to one another and not separated by a gap through which you can see the "background". Your character model might look like it jumps or teleports but the game checks the terrain below you to make sure you would normally be able to stand on it. This means that if the "invisible wall" separating where you are from where you want to go is thin enough the game places you on one side or the other at any given time.
2) You need line of sight but you don't appear to actually need vision. This applies when jumping up from a lower area to a higher one. If you are able to see where you start your movement from where you end it, it seems to allow you to complete your movement as intended. This means that your destination can actually be in the "fog of war" but you can't jump to the other side of a solid wall (since you can't see where you started from where you land).