Photonic neuromorphic system can simulate the neuromorphic algorithms with a speed of millions or billions multiples faster than the biological counterpart, which is better than electronics neuromorphic hardware system. It can be also capable of processing computing tasks more sophisticated than traditional optical computations. The photonic neuromorphic computing, exploring the adaptability, robustness and rapidity of ultrafast optical pulses, can overcome the scaling of digital optical computation and the noise accumulation of analog optical computation. The research progress on photonic neuromorphic computing is reported. Some essential theories and technologies, including photonic neuron, learning algorithms based on optical spiking pulses and the integrated photonic neuromorphic network framework, are introduced respectively. The necessity of research on photonic neuromorphic computing and its problems are discussed to present its potential applications in future.