With the rapid development of wireless communication technology and the emergence of intelligent applications, higher requirements have been put forward for data communication and computing capacity. Multi-access edge computing (MEC) can handle highly demanding applications by users by sinking the services and computing capabilities of the cloud to the edge of the cell. Meanwhile, the multiple input multiple output (MIMO) technology based on large-scale antenna arrays can achieve an order-of-magnitude improvement in system capacity. The introduction of MIMO into MEC takes full advantage of the energy and spectral efficiency of MIMO technology, providing a new computing paradigm for time-sensitive applications. In parallel, it can accommodate more users and cope with the inevitable trend of continuous data traffic explosion. In this paper, the state-of-the-art research status in this field is investigated, summarized and analyzed. Specifically, we first summarize a multi-base station cooperative mMIMO-MEC model that can easily be expanded to adapt to different MIMO-MEC application scenarios. Subsequently, we comprehensively analyze the current works, compare them to each other and summarize them, mainly from four aspects: research scenarios, application scenarios, evaluation indicators and research issues, and research algorithms. Finally, some open research challenges are identified and discussed, and these indicate the direction for future research on MIMO-MEC.