Scientists have been exploring the optical computing system for decades, in hoping that it will have faster speed and lower energy consumption to break the limitations of the traditional electronic computing system. However, due to the ineffective optical logic units, slow electronic interconnects, and lack of optical memory, the idea of the optical computing did not go too far and was eventually abandoned. In the era of big data, the flow and usage of information have been increased exponentially, which provides a unique opportunity for the rapid development of the silicon photonic technology. The heterogeneous integration of electronics and photonics on the same silicon substrate, the Silicon Photonics, ensures a wide-bandwidth, high-speed, low-cost, low energy-consumption, and application-oriented optoelectronic computing platform. Here, we review the recent efforts of computing using silicon photonic technology, including artificial neural network accelerators, heuristic solvers of nondeterministic polynomial problems, analog calculations, quantum logic processors, and neuromorphic photonics, and propose a computing structure based on silicon photonic platform to take the advantages of high speed optical parallel processing and high capacity optical interconnections at the same time. We expect the Silicon Photonics will be the best technology to solve the computing challenges and problems in the electronical or optical domain.