<p>In nature the crucial role of learning and memory is achieved with the help of synapses. The synapses which are plastic in nature, is formed with inter cellular connections of neurons, and the combination of these biological structures form the basic building blocks of neural networks. Synapses can change their state based on the neural activity of coupled neurons. The functionality of neurons and synapses is mimicked in hardware by utilizing very large scale integration technology, plays a key role in design of neuromorphic computing systems. The pathway to efficient neuromorphic computing systems is encoding the neural and synaptic functionalities in an electronic spin. One dominant technology that consistently features in the list of neuromorphic computing systems is spintronics (with the spin behavior of electrons). It shows the potentials to exploit energy efficiency, performance,reliability, magnetization using electric fields, and enhanced memory density of spintronics memory devices. This article provides a high level survey of the beyond Complementary Metal Oxide Semiconductor(CMOS) research with an emphasis on spintronic devices and focussed review on neuromorphic computing based on magnetic skyrmions. Here we review the latest progress in the domain of spintronic neuromorphic computing with the coherent presentation of ideas is provided. The survey stretch the wide-ranging expanse of spintronics-based neuromorphic computing systems, and the scheme is to point out current trends, evolving research issues and further directions on spintronics devices deployed on neuromorphic computing systems. We commence the discussion with a historical perspective, evolution, and subsequently, we make an in-depth survey of underlying components.</p>