Neuromorphic computing is a trending area in computer architecture which deals with the simulation of the brain on hardware. Machine learning problems are very complex to solve by a simple computer that works based on Von Neumann architecture, so we need to find architectures that are inspired by the brain and efficient for machine learning, artificial intelligence, and more complex applications. Neuromorphic computing deals with how the brain works; another thing is to find the material for simulating the brain on hardware and efficient algorithm for neuromorphic architecture. Simulating the working of neurons on hardware is very challenging because of the structure of neurons and communication mechanisms. In this paper, we have discussed the challenges in designing the communication mechanism for such neuromorphic computing when implemented in hardware. Each node in such hardware needs to multicast a message to many other nodes. The existing on-chip interconnects architectures are not enough to support such communication. We are presenting a survey on neuromorphic computing algorithms and architecture that have been proposed. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.