The enumeration of convex polytopes is a very old problem which could probably have its origin in Euler's famous theorem concerning the number of vertices, edges and faces of three dimensional polytopes. It is hard to characterize the face enumeration of general polytopes. But for simplicial polytopes, it is done in the so-called g-theorem, conjectured by MuMllen in 1970, and proved by Billera, Lee and Stanley. In this talk, we would like to present some backgrounds and progress of this theorem.