Spintronics is one of the growing research areas which has the capability to overcome the issues of static power dissipation and volatility suffered by the complementary metal-oxide-semiconductor (CMOS) industry. Magnetic tunnel junction (MTJ), one of the prominent spintronic devices, is not only used to develop the fully non-volatile-logic (NV-L) but combines magnetism and electronics to develop next-generation NVmemory (NV-M) and hybrid CMOS/MTJ circuits. To be specific towards hybrid CMOS/MTJ circuits, the fabrication of first hybrid full-adder in 2009, fabrication of MTJ based 240-tile NV-field programmable gate array (NV-FPGA) chip in 2013, fabrication of a 3000-6-input-LUTs based NV-FPGA chip in 2015, fabrication of MTJ based NV-logic-in-memory-large scale integration (NV-LIM-LSI) in 2017 and recently the fabrication of a full hybrid magnetic/CMOS System on Chip (SoC) under EU GREAT Project in 2019 has strengthened the belief and motivated the researcher to be continued in this domain. This review article aims to provide the complete design flow of hybrid CMOS/MTJ circuits developed using one of the fab compatible MTJ spintronic devices and its integration with conventional CMOS logic. The broad coverage of the article is MTJ construction, its switching mechanisms, a brief history of various compact models, reliability issues, and the concept of logic-in-memory (LIM) architecture. Finally, the article concludes with the challenges and future prospects of hybrid CMOS/MTJ circuits, which will motivate people in academia to cultivate research in this domain and industry to realize the prototype for a wide range of potential applications.