In traditional von Neumann computing architectures, the essential transfer of data between the processor and memory hierarchies limits the computational efficiency of next-generation system-on-a-chip. The emerging in-memory computing (IMC) approach addresses this issue and facilitates the movement of significant data and rapid computations. Among the different memory types, intrinsic energy efficiency is demonstrated by in-magnetic random access memory (MRAM) computing with a low-power spintronic magnetic tunnel junction device and hybrid integration at an advanced complementary metal-oxide semiconductor node. This study reviews state-of-the-art techniques for managing IMC with an emphasis on spin-transfer torque-MRAM computing via design schemes at the bit-cell, circuit, and system levels. In addition, this study presents effective design techniques and potential challenges and demonstrates the existing limitations of in-MRAM computing and potential methods for overcoming these issues. This study also considers the design technology co-optimization from the IMC perspective.