Regardless of the dimensionality the environment, movement is handled in a similar fashion in both cases (2D or 3D). Although there are many possible ways of implementing this, a pattern arises in each of these designs: simulation loop, integration, and collision detection. The details classify as engine development rather than AI, but an overview of the principles will come in handy later.
The game engine has to take into account movement requests from all the players and creatures in the world. The physics system is in charge of resolving the collisions with the environment as well as with other entities. Each of the data structures representing in-game objects will then be updated accordingly, with new velocities, positions, and orientations.
To date, animation systems take care of low-level limb "control" as predefined animation cycles (for example, walk and run) are combined to move the player's entire body. Such animation cycles can be chosen based on the higher-level control of the players. Therefore, characters in the game are not actually walking (active behavior), they are merely animated (passive process). This animation system requires a minimal amount of coordination with the physics system to prevent breaking the illusion with inconsistencies (for instance, walking on the spot when stuck against walls, running in midair).
For all intent and purposes, the low-level aspects of movement are abstracted from the player—greatly simplifying the process. This underlying layer can be referred to as a locomotion layer. Computer-controlled characters can also rely on such locomotive capabilities. Indeed, handling the movement for AI and human players together is becoming commonplace in game development now; it's a good way to reduce the amount of code by inheriting AI classes from human-player classes (that is, with the same locomotive functions).
In the near future, there are prospects of the AI taking over low-level limb control, done in a fully dynamic fashion. For human players, controls are unlikely to change as they often prove complex enough. Humans will just have to adjust to having the AI control their character's legs in the game! For nonplayer characters (NPCs), the AI could theoretically control the entire body as a whole, dealing with locomotion at the same time as high-level requests. However, keeping the locomotion separate has many advantages (for example, simplicity and little redundancy), so it is advantageous to retain this distinction in the future.