Recent advancement of deep learning has been elevated the multifaceted nature in various applications of this field. Artificial neural networks are now turning into a genuinely old procedure in the vast area of computer science; the principal thoughts and models are more than fifty years of age. However, in this modern computing era, 3rd generation intelligent models are introduced by scientists. In the biological neuron, actual film channels control the progression of particles over the layer by opening and shutting in light of voltage changes because of inborn current flows and remotely led to signals. A comprehensive 3rd generation, Spiking Neural Network (SNN) is diminishing the distance between deep learning, machine learning, and neuroscience in a biologically-inspired manner. It also connects neuroscience and machine learning to establish high-level efficient computing. Spiking Neural Networks initiate utilizing spikes, which are discrete functions that happen at focuses as expected, as opposed to constant values. This paper is a review of the biological-inspired spiking neural network and its applications in different areas. The author aims to present a brief introduction to SNN, which incorporates the mathematical structure, applications, and implementation of SNN. This paper also represents an overview of machine learning, deep learning, and reinforcement learning. This review paper can help advanced artificial intelligence researchers to get a compact brief intuition of spiking neural networks.