Neuromemristive circuits represent a new paradigm in the field of neuromorphic computing wherein memristive devices are used as artificial synapses. The primary benefit of these devices is that they take advantage of material properties to emulate the temporal and biophysical properties of biological neural elements. Memristors under their state-dependent non-linear properties can mimic the biological synaptic behavior of co-localized memory and processing abilities. Besides, memristors have also been reported to replicate biological learning rules like spike-timing-dependent plasticity. This paper focuses on one class of memristors based on resistive switching caused by nano ionic redox processes. The operation, classification, and key behaviors are discussed while taking into consideration the key challenges that are encountered in their synaptic implementations. © 2020 IEEE.