so the walking in a terrain feature should be delegated to the physics engine?
There are several sub-systems involved.
a.) AI (for the NPCs) for path finding: What way to go to reach the target location? As frob has mentioned, this can be solved by using a dedicated mesh.
b.) Animation blend controlling: Set by AI or player input, which kind of motion is used (walking, running, ...).
c.) Animation playback: How is the character posed at time.
d.) Collision correction: reacting on obstacles and ground.
Details depend on the kind of game and character implementation, of course. Assuming a 3D world with skeleton based characters...
Things are relatively easy if you are willing to accept some artifacts like foot sliding and averaged slopes and steps in terrain. It is not easy to get rid of those issues. A locomotion sub-system for foot placement is one possible undertaking. Foot sliding alone can also be reduced to a minimum if the animation playback is not controlled by time but by the made way; e.g. the Wolfire engine follows such a approach. So, for completeness we need to add:
e.) Locomotion control: foot placement and pose controlling.
However, most games especially in the hobby area do not deal with such complex things like locomotion.