The advancement of photonic integrated circuits (PICs) brings the possibility to accomplish on-chip optical interconnects and computations. Optical computing, as a promising alternative to traditional CMOS computing, has great potential advantages of ultra-high speed and low-power in information processing and communications. In this paper, we survey the current research efforts on optical computing demonstrated on silicon-on-insulator-based PICs. The advantages, limitations, and possible research directions for further investigation are discussed.