Abstract: Given a d-dimensional convex polytope, its k-th face number is the number of (k 􀀀-1)-dimensional faces it has. The f-vector of a polytope is the sequence of its face numbers. Beside Euler's formula, these numbers satisfy further equalities and inequalities. Characterization of f-vector of d-dimensional convex polytope is already known for d ≤ 3 . For d ≥ 3, we do not have a complete answer, but g-theorem gives us a characterization for simplicial (and dually simple) case. Here we review g-theorem and its various proofs.