With the advent and continuous development of the Internet of Things era, a large number of emerging applications, such as driverless, have emerged. Usually such applications need to consume a lot of computing resources and have high demand for low latency and data processing. However, the limited computing power of the devices themselves cannot meet the low latency and other needs of emerging applications, which limits the further development of IoT. Mobile edge computing (MEC) is an emerging computing paradigm where mobile devices interact directly with MEC platforms at the network edge and offload computational tasks to MEC servers to solve the problem of limited device resources. In this paper, we conduct an in-depth study of the computational offloading problem in mobile edge computing, and provide an in-depth and comprehensive summary of the current status and results of the research on MEC-oriented computational offloading strategies. First, the MEC technology and its typical application scenarios are introduced; then, the computation offloading strategy with optimized time, energy consumption, and hybrid goals for system performance gain is introduced from two aspects: single-user computation offloading and multi-user computation offloading.