In the fourth industrial revolution, the efficient processing of huge amounts of data is important due to the development of artificial intelligence (AI), internet of things (IoT), and machine learning (ML). The conventional computing system, which is known as von Neumann architecture, has been facing bottleneck problems because of the physical separation of memory and central processing unit (CPU). Many researchers have interested to study on neuromorphic computing, inspired by the human brain, to solve the bottleneck problems. The development of artificial neuromorphic devices, such as neuron and synaptic devices, is important to successfully demonstrate a neuromorphic computing hardware. Various Si CMOS transistor-based circuits have been investigated to implement the behaviors of the biological neuron and synapse; however, they are not suitable for mimicking the large-scale biological neural networks because of Si CMOS transistor’s scalability and power consumption issues. In this report, we review the recent research progress in artificial neurons and synaptic devices based on emerging materials and discuss the future research direction of artificial neural networks.