The spin-based memory, spin transfer torque-magnetic random access memory (STT-MRAM), has the potential to enhance the power efficiency of high density memory systems. Its desirable characteristics include nonvolatility, fast operation, and long endurance. However, dry etching of MRAM structures remains a challenge as the industry is ramping up its production. In this paper, we explore the etching strategies that have been used to etch the MRAM structures. Several etching techniques have been developed to attain optimal device performance. These are reactive ion etching, time modulated plasma etching, atomic layer etching, and ion beam etching. Sidewall profile, sidewall contamination or damage, redeposition, selectivity, and noncorrosiveness are the main factors to consider while selecting the best etching methods. This paper starts with the fundamentals of MRAM reading, writing, and storing principles and finishes with the current approaches to solve the etch challenges. For etching, the most commonly used magnetic materials such as CoFeB, CoFe, and NiFe are covered in this article.