Silicon is a nonlinear material and optics based on silicon makes use of these nonlinearities to realize various functionalities required for on-chip communications. This article describes foundations of these nonlinearities in silicon at length. Particularly, self phase modulation and cross phase modulation in the context of integrated on-board and on-chip communications are presented. Important published results and principles of working of these nonlinearities are presented in considerable detail for non-expert readers.