Brain Inspired Computing (BIC) is an emerging research field that aims to build fundamental theories, models, hardware architectures, and application systems toward more general Artificial Intelligence (AI) by learning from the information processing mechanisms or structures/functions of biological nervous systems. It is regarded as one of the most promising research directions for future intelligent computing in the post-Moore era. In the past few years, various new schemes in this field have sprung up to explore more general AI. These works are quite divergent in the aspects of modeling/algorithm, software tool, hardware platform, and benchmark data, since BIC is an interdisciplinary field that consists of many different domains, including computational neuroscience, artificial intelligence, computer science, statistical physics, material science, microelectronics and so forth. This situation greatly impedes researchers from obtaining a clear picture and getting started in the right way. Hence, there is an urgent requirement to do a comprehensive survey in this field to help correctly recognize and analyze such bewildering methodologies. What are the key issues to enhance the development of BIC? What roles do the current mainstream technologies play in the general framework of BIC? Which techniques are truly useful in real-world applications? These questions largely remain open. To address the above issues, in this survey we first clarify the biggest challenge of BIC: how can AI models benefit from the recent advancements in computational neuroscience? With this challenge in mind, we will focus on discussing the concept of BIC and summarize four components of BIC infrastructure development: 1) modeling/algorithm; 2) hardware platform; 3) software tool; and 4) benchmark data. For each component, we will summarize its recent progress, main challenges to resolve, and future trends. On the basis of these studies, we present a general framework for the real-world applications of BIC systems, which is promising to benefit both AI and brain science. Finally, we claim that it is extremely important to build a research ecology to promote prosperity continuously in this field.