The modern-day computing technologies are continuously undergoing a rapid changing landscape; thus, the demands of new memory types are growing that will be fast, energy efficient and durable. The limited scaling capabilities of the conventional memory technologies are pushing the limits of data-intense applications beyond the scope of silicon-based complementary metal oxide semiconductors (CMOS). Resistive random access memory (RRAM) is one of the most suitable emerging memory technologies candidates that have demonstrated potential to replace state-of-the-art integrated electronic devices for advanced computing and digital and analog circuit applications including neuromorphic networks. RRAM has grown in prominence in the recent years due to its simple structure, long retention, high operating speed, ultra-low-power operation capabilities, ability to scale to lower dimensions without affecting the device performance and the possibility of three-dimensional integration for high-density applications. Over the past few years, research has shown RRAM as one of the most suitable candidates for designing efficient, intelligent and secure computing system in the post-CMOS era. In this manuscript, the journey and the device engineering of RRAM with a special focus on the resistive switching mechanism are detailed. This review also focuses on the RRAM based on two-dimensional (2D) materials, as 2D materials offer unique electrical, chemical, mechanical and physical properties owing to their ultrathin, flexible and multilayer structure. Finally, the applications of RRAM in the field of neuromorphic computing are presented. © 2023, The Author(s).