Memristive devices have recently garnered significant attention to closely mimic synaptic and neuron functions for neuromorphic computing due to their prominent advantages, including simple structure, low power consumption, and rich resistive switching dynamics. In this chapter, we will introduce the device structure, materials, and switching behaviors of memristive devices. Also, the switching mechanisms mainly related to formation/rupture of conductive filaments and modulation of interfacial barrier will be described in detail to help understand the switching dynamics of memristive devices. Then, state-of-art memristive synapses and neurons will be discussed. Finally, experimental demonstrated memristive neural networks also will be briefly introduced here.