As the research on artificial intelligence booms, there is broad interest in braināinspired computing using novel neuromorphic devices. The potential of various emerging materials and devices for neuromorphic computing has attracted extensive research efforts, leading to a large number of publications. Going forward, in order to better emulate the brain's functions, its relevant fundamentals, working mechanisms, and resultant behaviors need to be reāvisited, better understood, and connected to electronics. A systematic overview of biological and artificial neural systems is given, along with their related critical mechanisms. Recent progress in neuromorphic devices is reviewed and, more importantly, the existing challenges are highlighted to hopefully shed light on future research directions.