The high directionality and short wavelength of laser transmission in space make it a promising direction for the next generation of satellite laser communication. The laser intersatellite communication can achieve high quality-of-service satellite communication with high transmission speed, wide bandwidth, and high security, which can even improve the precision of satellite ranging in space. The establishment of a satellite backbone network with laser intersatellite links can achieve global management and control of satellites, greatly improve its independence from the ground system, and expand the communication capacity. Due to its advantages in improving the survivability, autonomy, mobility and flexibility of satellite networks, the domestic "Star Network", "Hongyan", "Hongyun", "Xingyun" and "Space-Earth Integration" constellations and foreign "Kuiper", "Telesat" and "Starlink" networks have integrated laser intersatellite links as one of its core transmission link methods, laser communication terminals also become one of the standard spacecraft payloads. It is foreseeable that intersatellite communication will continue to develop and transform from the radio wave era to the laser era, which makes the survey on laser intersatellite links meaningful.This paper first introduces the technical fundaments, including the link establishment modes, link modulation modes, and wavelengths. The intersatellite laser link establishment mainly relies on three steps of pointing, acquiring, and tracking, comprehensively called PAT system. The link modulation modes include non-coherent and coherent communications. Compared with the non-coherent system, the coherent system has the advantages of high spectral efficiency. For medium and high-orbit satellites that need to carry more complex and sophisticated communication tasks, the laser intersatellite link is mostly modulated by the coherent communication system. Conversely, low-orbit satellite laser communication and deep space exploration projects mainly use non-coherent modulation mode. To reduce the impact of the solar background and solar scattering, the current laser communication mainly considers the selection in the range of 500 nm to 2 000 nm. Since ground industrial-grade laser components mostly use 1 550 nm wavelength laser as the standard preparation, the communication technology can be migrated to the satellite network at a relatively low cost. With the development of technology, the communication systems of various countries are developing in a more compatible direction, that is, compatible with both 1 064 nm and 1 550 nm wavelengths. Countries have successfully carried out a number of on-orbit technology verifications in the field of inter-satellite laser communication, and have entered the stage of large-scale application. The survey finds that the current on-orbit technology verification uses customized laser terminals to meet the specific needs of various tasks. Companies such as Mynaric, Hyperion Tech, Thales Alenia Space, and NICT have begun to launch laser terminal products with higher speed, smaller mass and volume, and lower power consumption. These terminal products can adapt to the universal requirements of similar multi-task. According to the different mission requirements of different orbit heights, this paper summarizes the current development status and plans of laser communication achievements since 2015 (Tab.1). Through the comprehensive survey, this paper reveals the flexibility and modularity trends of laser communication terminals, and four development trends of satellite laser communication: standardization, compatibility, networking, and commercialization. In addition to being used as a carrier for information interaction, laser ranging can obtain more accurate intersatellite ranging values, stronger anti-interference and anti-eavesdropping capabilities compared to traditional RF ranging solutions. The end of this paper surveys on prospects of satellite laser ranging applications, which intends to provide reference to the domestic development and research of laser-based satellite technology.The laser intersatellite link is developing vigorously. At the same time, the mission requirements of the satellite network are complex and diverse. For satellites of different orbits and mission types, the selection of the communication system, wavelength, and access mode of the laser intersatellite link needs to be analyzed in detail according to each situation. The research aims to provide some reference for the design and optimization of laser inter-satellite links in the future. It is expected that building a standardized, compatible, networked and commercialized laser intersatellite link will help maximize space resources and interconnection of satellite networks.