Although artificial intelligence (AI) has achieved many feats at a rapid pace, there still exist open problems and fundamental shortcomings related to performance and resource efficiency. Since AI researchers benchmark a significant proportion of performance standards through human intelligence, cognitive sciences-inspired AI is a promising domain of research. Studying cognitive science can provide a fresh perspective to building fundamental blocks in AI research, which can lead to improved performance and efficiency. In this review paper, we focus on the cognitive functions of perception, which is the process of taking signals from one's surroundings as input, and processing them to understand the environment. Particularly, we study and compare its various processes through the lens of both cognitive sciences and AI. Through this study, we review all current major theories from various sub-disciplines of cognitive science (specifically neuroscience, psychology and linguistics), and draw parallels with theories and techniques from current practices in AI. We, hence, present a detailed collection of methods in AI for researchers to build AI systems inspired by cognitive science. Further, through the process of reviewing the state of cognitive-inspired AI, we point out many gaps in the current state of AI (with respect to the performance of the human brain), and hence present potential directions for researchers to develop better perception systems in AI.