The spiking neural network, which is called the third generation of artificial neural network, is the best neuromorphic algorithm to imitate human brain. Compared with the traditional artificial neural networks, the spiking neural networks are hardware-friendly and highly energy-efficient. Furthermore, the optical spiking neural networks are high speed, low energy consumption, low delay, high parallelism, and anti-electromagnetic interference, compared with the electronic spiking neural networks. The origin of optical spiking neural networks are introduced in this paper. The research advances, existing problems and challenges are illustrated from the aspect of the optical spiking neurons, framework of optical spiking neural networks and the corresponding training algorithms. The perspectives of the optical spiking neural networks are also analyzed.