The notion of q-Schur algebras is introduced in terms of flag varieties for any finite and affine type. These algebras can be regarded as a generalization of Hecke algebras. In this talk, we shall formulate their cells and give a q-Schur algebra analog of Lusztig's properties (P1)-(P15) for cells in Hecke algebras. We also show that these q-Schur algebras of finite type are cellular, which is a generalization of Geck's theorem on cellularity of Hecke algebras.