Resistive random-access memory(RRAM),also known as memristors,having a very simple device structure with two terminals,fulfill almost all of the fundamental requirements of volatile memory,nonvolatile memory,and neuromorphic charac-teristics.Its memory and neuromorphic behaviors are currently being explored in relation to a range of materials,such as biolo-gical materials,perovskites,2D materials,and transition metal oxides.In this review,we discuss the different electrical behavi-ors exhibited by RRAM devices based on these materials by briefly explaining their corresponding switching mechanisms.We then discuss emergent memory technologies using memristors,together with its potential neuromorphic applications,by eluci-dating the different material engineering techniques used during device fabrication to improve the memory and neuromorph-ic performance of devices,in areas such as/ON//oFF ratio,endurance,spike time-dependent plasticity(STDP),and paired-pulse facili-tation(PPF),among others.The emulation of essential biological synaptic functions realized in various switching materials,in-cluding inorganic metal oxides and new organic materials,as well as diverse device structures such as single-layer and multilay-er hetero-structured devices,and crossbar arrays,is analyzed in detail.Finally,we discuss current challenges and future pro-spects for the development of inorganic and new materials-based memristors.