One step block implicit methods (BIM) have desirable stability properties and provide higher-order of accuracy. Moreover, BIM offer additional parallelism in time and are more suitable for large scale parallel computers with a large number of processor cores than the traditional time integration methods that are only parallel in space. In this talk, we first present a family of BIM developed on uniform and non-uniform meshes. Then we study these methods under a unified framework by employing a BIM tableau including two matrices and two vectors.  Further, we show that the traditional finite element theory for parabolic problems discretized by the backward Euler or Crank-Nicolson schemes can also be extended for BIM.. Finally, some numerical results obtained on a parallel computer with thousands of processors are reported to demonstrate the effectiveness of BIM.