Neuromorphic electronics, an emerging field that aims for building electronic mimics of the biological brain, holds promise for reshaping the frontiers of information technology and enabling a more intelligent and efficient computing paradigm. As their biological brain counterpart, the neuromorphic electronic systems are complex, having multiple levels of organization. Inspired by David Marr's famous three‐level analytical framework developed for neuroscience, the advances in neuromorphic electronic systems are selectively surveyed and given significance to these research endeavors as appropriate from the computational level, algorithmic level, or implementation level. Under this framework, the problem of how to build a neuromorphic electronic system is defined in a tractable way. In conclusion, the development of neuromorphic electronic systems confronts a similar challenge to the one neuroscience confronts, that is, the limited constructability of the low‐level knowledge (implementations and algorithms) to achieve high‐level brain‐like (human‐level) computational functions. An opportunity arises from the communication among different levels and their codesign. Neuroscience lab‐on‐neuromorphic chip platforms offer additional opportunity for mutual benefit between the two disciplines.