Deep space exploration is the cornerstone of humanity to explore and understand the universe, and it is one of the frontier fields of scientific research. Deep space communication serves as the information bridge that establishes contact between deep space detectors and Earth, acting as a spatial link to ensure the successful completion of deep space exploration missions. The communication system that uses lasers as carrier, characterized by high communication rates, small size, and light weight, has become the main direction for the future development of deep space communication and has also become an international research hotspot in recent years. The article summarizes the characteristics of deep space optical communication technology. Deep space laser communication has the following features: long link distance, significant space loss, extended transmission delay, non-cooperative pointing acquisition and tracking, high relative velocity, large point ahead angle, substantial Doppler frequency shift, and long mission duration. Using examples such as LLCD, DSOC, O2O, LunaNet, OPTEL-D, and DOCS, the article provides a detailed overview of the development trends, latest research progress, and future plans in deep space laser communication technology across the United States, Europe, and China. In the future, deep space laser communication will continue to evolve towards longer communication distances, network integration, terminal miniaturization, integration and type serialization. Key areas of focus include ultra-long-distance PAT, high photon utilization modulation and coding, high-power optical emission, terrestrial large-aperture optical antenna, and ultra-sensitive single-photon reception. The article concludes with a summary and prospects, offering valuable insights for the development of deep space laser communication and interstellar laser communication networks in China. Both the United States and Europe have been pioneers in deep space laser communication technology research. They have conducted in-orbit technology verification for lunar-to-Earth laser communication and achieved breakthroughs in several key technologies related to deep space laser communication. In contrast, domestic deep space laser communication in China is still in its early stages. Laser communication is an inevitable choice for the future development of deep space communication and is a crucial component of space exploration activities. The moon is the closest celestial body to the earth, carrying out the moon - earth laser communication will provide a more efficient means of data transmission for lunar exploration. Additionally, this effort contributes to building a solid technological foundation for more distant deep space laser communication, marking the first step in China’s research on deep space laser communication technology. Simultaneously, China has initiated planetary exploration projects, and future plans include launching missions to more distant targets such as asteroids and Mars sample return missions. To ensure the successful completion of these long-distance exploration tasks, establishing a matching deep space communication capability is of paramount importance. As laser communication technology continues to evolve, deep space laser communication will become a critical component of the interstellar internet. It will play essential roles in interstellar backbone networks, extension networks, and planetary networks. Furthermore, the development of deep space laser communication complements space optical communication network technologies, mutually reinforcing each other. Ultimately, this progress will lead to the establishment of a near-Earth laser communication network based on ground stations and near-Earth orbit satellites, which will serve as the foundation for an interstellar laser communication network.