Abstract: The fast and low-power in-memory computing architecture, which integrates memory and calculation, breaks through the traditional von-Neumann system that separates memory and calculation, and solves the problem of “memory wall” that limits the arithmetic power of the processor, which has become a research hotspot of new computing architecture. The basic devices for in-memory computing include fast and mature static random access memory (SRAM), low power, fast response and non-volatile memristor, and high density, low static power and non-volatile magnetic random access memory (MRAM). Up to the present, a great variety of in-memory computing studies have been proposed based on these devices, however, a systematic and comprehensive literature review on these in-memory computing architectures is still missing. In this paper, we firstly introduce the in-memory computing principles of different devices, the current development status of in-memory computing architectures, and the practical application scenarios from the three directions of SRAM, memristor, and MRAM. Next, the existing solutions and the future directions for the problems and challenges of current in-memory computing architectures are given. Finally, we summarize the research focus of in-memory computing based on the above devices, outline the shortcomings of the current research, and look forward to the future development direction.