basic game engine concept

i just wonder with the different APIs available like Directx or Opengl which can do all the work right from defining points to rendering complex scenes, where does the "game engine" fit in? what tasks should it handle? what tasks should the game handle and what tasks should be left for the API? i have some knowledge about opengl but in bits and pieces. What i need are sites where everything about the Opengl and the math behind 3d is explained in detail and when i say !! EVERYTHING !! i mean it. Also any inspirational opensource engines out there which will get me started ??