Neuromorphic computing, an emerging non-von Neumann computing mimicking the physical structure and signal processing technique of mammalian brains, potentially achieves the same level of computing and power efficiencies of mammalian brains. This chapter will discuss the state-of-the-art research trend on neuromorphic computing with memristors as electronic synapses. Furthermore, a novel three-dimensional (3D) neuromorphic computing architecture combining memristor and monolithic 3D integration technology would be introduced; such computing architecture has capabilities to reduce the system power consumption, provide high connectivity, resolve the routing congestion issues, and offer the massively parallel data processing. Moreover, the design methodology of applying the capacitance formed by the through-silicon vias (TSVs) to generate a membrane potential in 3D neuromorphic computing system would be discussed in this chapter
