“Spintronics” refers to the understanding of the physics of electron spin-related phenomena. While most of the significant advancements in this field has been driven primarily by memory, recent research has demonstrated that various facets of the underlying physics of spin transport and manipulation can directly mimic the functionalities of the computational primitives in neuromorphic computation, i.e., the neurons and synapses. Given the potential of these spintronic devices to implement bio-mimetic computations at very low terminal voltages, several spin-device structures have been proposed as the core building blocks of neuromorphic circuits and systems to implement brain-inspired computing. Such an approach is expected to play a key role in circumventing the problems of ever-increasing power dissipation and hardware requirements for implementing neuro-inspired algorithms in conventional digital CMOS technology. Perspectives on spin-enabled neuromorphic computing, its status, and challenges and future prospects are outlined in this review article.