The large amount of unstructured data generated by the Internet of Things and cloud computing has recently increased the demand for data computing power and energy efficiency. Referencing the information processing method of the biological brain with neuron and synapse as basic units, neuromorphic computing can simulate the biological nervous system from the aspects of interconnection architecture and information processing mode, and realize ultra-low power processing of real-time information, which have become the forefront of the development of computing technology in the big data era. The processing of computational data in the optical domain makes photonic neuromorphic computing research important owing to its high application potential. On the one hand, photonic neuromorphic computing can take advantage of high-speed transmission, low power consumption, and high parallelism of photons. On the other hand, it can also prevent photoelectric and electro-optic conversion, thus, reducing additional time and power consumption. In recent years, phase-change materials (PCM), as a kind of optical material with high refractive index contrast and non-volatile property, whose refractive rate can be continuously adjusted under the driving of optical, electrical, and thermal excitations, have provided a feasible solution for non-volatile photonic neuromorphic computing and have become the current research hotspot. In this paper, we first introduce the basic principle and implementation method of photonic neuromorphic computing. Subsequently, we discuss the principle of utilizing phase-change materials in photonic neuromorphic computing. According to the unique characteristics of phase-change materials selected in different implementation schemes, two kinds of phase-change materials and different applications of optical synapse devices and integrated arrays are then summarized. Finally, we prospect the development of photonic neuromorphic computing techniques based on phase-change materials.