In this information era with bursting data, there are three fundamental problems limiting the further development of computing power: The gradually slowing down of Moore’s law, the rapidly increasing energy consumption while scaling down, and the restriction of data transfer between separated memory and processor known as “Von Neumann bottleneck”. To deal with massive data and make all things in our daily life interconnected, it is imperative to develop new generation of computing paradigms, for example, neuromorphic computing. Inspired by the human brain, neuromorphic computing has drawn extensive attention in recent years due to its high parallelism, low power consumption and in-memory computation, especially when the tide of artificial intelligence is sweeping across the globe now. Novel neuromorphic devices are key to the construction of neuromorphic computing systems, providing an efficient implementation of artificial neural network on chip. Besides, by simulating the behavior of biological neurons and synapses at the physical level, neuromorphic devices can enable a brand new computing method, which is thought to be an essential and promising way to build a brain-like system on chip. This paper focuses on the current research progresses and future research trends of neuromorphic devices. It summarizes the physical mechanisms of neuromorphic devices, according to which they can be divided into ion-migration device, material phase change device, electron-migration device, magnetic device and so on. It further details the inner dynamics happened in a single device by characterizing the changing process in transmission electron microscope. This paper also explains how these neuromorphic devices can be used for computing, where memristor, as the missing fourth basic circuit component, is used as a theoretical support. Through making up a crossbar structure, these devices can directly calculate vector-matrix multiplication by Ohm’s law and Kirchhoff’s law. It is an elegant way that can accelerate artificial neural network in parallel by computing in memory. In addition, exploiting the intrinsic dynamics in the devices can realize complex and interesting functions of biological neural networks, such as long-term plasticity, short-term plasticity and spike timing dependent plasticity. For example, a synaptic transistor based on two-dimensional materials WSe2 can simulate the biologically transport process of calcium ion, leading precisely regulated coexistence of long-term and short-term memory. Remarkably, a significant advance is realizing heterosynaptic plasticity, a general mode in brain’s cortical network, in a single multi-terminal device, which is crucial for biologically plausible supervised learning on hardware. Furthermore, artificial neurons composed of memristors and capacitors have some natural advantages compared to traditional circuits, containing rich dynamics for neuromorphic computing, such as stochasticity, adaptive threshold and chaotic oscillation. Recently, materials with new mechanisms, like ferroelectric materials, are also being explored to realize complex neuron functions, contributing to less power and smaller area. By devices and algorithms co-design, it is time to explore the next generation of neural network, transforming current processing unit to a more efficient and intelligent brain-inspired style. As a conclusion, the outstanding challenges and trends in the field of neuromorphic devices are discussed in this paper. These researches are promising for building a neuromorphic computer in the future, which will be complementary to classical computer and outperform in many tasks.