In recent years, the rapid growth of big data and the increasing demand for high-performance computing have fueled the development of novel computing architectures. Among these, in-memory computing architectures that leverage the high-density and low-latency nature of modern memory technologies have emerged as promising solutions for domain-specific computing applications. STT-MRAM (Spin Transfer Torque Magnetic Random Access Memory) is one such in-memory computing technology that holds great potential for this field due to its non-volatility, high endurance, and low power consumption. In this survey paper, we aim to provide a comprehensive overview of the state-of-the-art in STT-MRAM-based domainspecific in-memory computing (DS-IMC) architectures. We examine the challenges, opportunities, and trade-offs associated with these architectures from the perspective of various application domains, like machine learning, image and signal processing, and data encryption. We explore different experimental research tools used in studying these architectures, guidelines for efficiently designing them, and gaps in the state-of-the-art that necessitate future research and development.INDEX TERMS domain-specific architectures, in-memory computing, spin-transfer torque RAM.