Unreal Tournament is one example of a few games that allow mod authors to change the physics of the game because everything other than the basic collision detection is not in the game's engine but in the game's code itself. We'll get into more of that later. Because games require something external to control your character, the engine must also handle the input. The game engine has to be able to recognize and deal with a keyboard, a mouse, a joystick, or any other peripheral the user might need to control the character. The engine also handles aesthetic details like the game's animation system.
Some games use a skeletal animation system, while some use a mesh-based system.
Both of these are very different from a technical standpoint, and the engine does the work of implementing them. Textures are then used to decorate the game and give it the look the player sees. If polygons were the clay, textures would be the paint applied to it to decorate it after firing it. The renderer itself is a very complex segment of the engine that consists of several subsections, including things like lighting, geometry, and particle systems. While these are the basic aspects covered by most 3D game engines, not every engine handles these in the same way.