Neuromorphic computing, which imitates the principle behind biological synapses with a high degree of parallelism, has recently emerged as a promising candidate for novel and sustainable computing technologies. The first step toward realizing a massively parallel neuromorphic system is to develop an artificial synapse capable of emulating synapse functionality, such as analog modulation, with ultralow power consumption and robust controllability. We begin this chapter with a simple description of neuromorphic systems and memristor synapses. Further, we introduce and evaluate the state-of-the-art neuromorphic hardware technology in terms of novel functional materials and device architectures toward the implementation of fully neuromorphic computers, which have been extensively explored in recent years. Finally, we briefly describe artificial neural networks based on memristor synapse in forms of crossbar arrays.Conventional computing architecture, that is, von Neumann architecture, forms the groundwork for modern computing technologies [3,18]. Despite tremendous growth in computing performance, classical architecture currently suffers from the von Neumann bottleneck, which results from data movements between the processor and the memory unit [4,5]. The memory wall issue, causing high power consumption and low speed, hinders the continuous development of computing technologies [4,5,9]. Moreover, artificial neural network (ANN) algorithms, such as deep learning [19], deal with image classification [20,21], sound recognition [22,23], specific complex tasks (e.g., the AlphaGo [24]) and so on. Although the ANN algorithms have exhibited superior performance over the conventional computing technologies, they are, at present, constructed on the von Neumann architecture; hence, considerable time and energy resources are required for their operation [8,9]. Neuromorphic architecture [6,7], a bio-inspired computing architecture, is one of the most promising candidates to resolve these problems. The neuromorphic systems take advantage of the cerebral nervous system, which consists of a massive parallel connectivity between the neurons (i.e., processor) and the synapses (i.e., memory), indicating the absence of the von Neumann bottleneck [8,9]. Figure 1 shows the shift of the computing architecture from von Neumann architecture (Figure 1a) to neuromorphic architecture (Figure 1b). The von Neumann architecture shows that the processor and memory are separate, leading to the von Neumann bottleneck. In contrast, in the case of neuromorphic architecture, the neurons and synapses are combined, alleviating the bottleneck issue. The neurons are uncomplicated computing units, the synapses are local memory units, and the communication channels (red line) connect numerous neurons and synapses. It should be noted that the practical purpose of neuromorphic systems is not to replace the von Neumann architecture completely, but to supplement the conventional architecture to make up its leeway, especially for intelligent tasks such as image r...