Computing systems are widely used in medical diagnosis, climate prediction, autonomous vehicles, etc. As the key part of electronics, the performance of computing systems is crucial in the intellectualization of the equipment. The conflict between performance, efficiency, and cost can be solved by choosing an appropriate computing system architecture. In order to provide useful advice and instructions for the designers to fabricate high-performance computing systems, this paper reviews the Chiplet-based computing system architectures, including computing architecture and memory architecture. Firstly, the computing architecture used for high-performance computing, mobile, and PC is presented and summarized. Secondly, the memory architecture based on mainstream memory and emerging non-volatile memory used for data storing and processing are introduced, and the key parameters of memory are compared and discussed. Finally, this paper is concluded, and the future perspectives of computing system architecture based on Chiplet are presented.