Mobile devices are increasingly interacting with clouds, and mobile cloud computing has emerged as a new paradigm. An central topic in mobile cloud computing is computation partitioning, which involves partitioning the execution of applications between the mobile side and cloud side so that execution cost is minimized. This paper discusses computation partitioning in mobile cloud computing. We first present the background and system models of mobile cloud computation partitioning systems. We then describe and compare state-of-the-art mobile computation partitioning in terms of application modeling, profiling, optimization, and implementation. We point out the main research issues and directions and summarize our own works.