With the exponential growth of global data traffic in the internet era, the demand of ultra-high-speed communications is becoming increasingly urgent. Because of its huge available bandwidth resources,terahertz communication has become one of the key technical approaches for the next generation of ultra-high-speed wireless communications. Terahertz communication systems can be divided into two types: the systems based on electronics technology and those based on photonics-assisted technology. The latter has some unique advantages, such as high communication rate, flexible frequency tunability, and seamless integration with optical fiber access networks. The basic principles of typical photonics-assisted terahertz communication systems are introduced firstly. Then, under these basic principles, the research progresses of signal generation and reception, multi-dimensional multiplexing and probabilistic constellation shaping in the systems are reviewed. Finally, the developing problems need to be solved in the photonics-assisted terahertz communication system are discussed.