The strong optical nonlinearity of silicon and tight optical field confinement in silicon waveguides, accompanied by silicon's unique material properties such as high optical damage threshold and thermal conductivity, enable compact nonlinear photonic devices to be fabricated in silicon using cost effective CMOS compatible fabrication technology. By integrating a p-i-n diode into the silicon waveguide, the nonlinear optical loss due to two photon absorption induced free carrier absorption in silicon waveguides can be dramatically reduced, and efficient nonlinear optical devices can be realized on silicon chips for high speed optical communications. In this paper, we report recent development of silicon p-i-n waveguide based nonlinear photonic chips for wavelength conversion and dispersion compensation applications. Wavelength conversion efficiency of -8.5 dB can be achieved in an 8-cm long p-i-n silicon waveguide by four-wave mixing in continuous-wave operation, and chromatic dispersion compensation by mid-span spectral inversion is demonstrated experimentally using silicon spectral inverter at the mid-span of a fiber optical link, achieving transmission of optical data at 40 Gb/s over 320 km of standard fiber with negligible power penalty. The unique advantages of using silicon over previously proposed nonlinear optical media for dispersion compensation are discussed.