Unlike their ground-based counterparts, space-borne laser interferometer gravitational wave detection missions focus on the gravitational wave sources in the lower frequency band between 0.1 mHz and 1 Hz. Various gravitational wave sources in such a frequency band are believed to be of considerable interest in astronomy and cosmology. The typical gravitational wave sources of a space-borne laser interferometer gravitational wave antenna are the super (intermediate) mass black hole merger, extreme (intermediate) mass ratio in-spiral, galactic binaries of compact stars, and stochastic gravitational wave background. The gravitational wave sources within the 0.1 mHz-1 Hz frequency band can help us understand the mystery of the universe's structural formation, evolution of massive black holes and its harbored galaxies, nature of gravity near the horizon of these massive black holes, and history of the early universe beyond the cosmic microwave background. To design a mission to achieve the abovementioned scientific impacts, considerable attention should be paid to several issues, such as orbital design and arm-length choice. The success of a space-borne laser interferometer gravitational wave detection mission requires a pico-meter precision inter-satellite laser ranging interferometer system and a state-of-the-art drag-free control system because of the weakness of the gravitational wave signals. The inter-satellite laser ranging interferometer system comprises four subsystems: stable laser source, stable laser telescope, ultra-precise laser interferometer, and ultra-precise phasemeter. Techniques, such as arm-locking, time-delay interferometry, sideband scheme, differential wave-front sensing, and pointing control, should be employed to suppress the laser frequency noise, clock frequency noise, and laser pointing jitter noise. Additionally, the ultra-precise laser interferometer needs to integrate the following functionalities: laser acquisition, laser ranging, laser communication, and clock synchronization. Conversely, the drag-free control system has the following three components: inertial sensor, micro-thruster, and drag-free controller. The inertial sensor is used to sense the displacement between the spacecraft and proof mass and send the signal to the drag-free controller. Further, the controller commands the micro-thruster to push the spacecraft to maintain the proof mass' position centered at the electrostatic cage of the inertial sensor. The space laser interferometer gravitational wave antenna is also a highly complex system in debt of the high degree of coupling between a subsystem and the high confusion of the enormous quantity of signals. An end-to-end numerical simulator might be essential in helping us understand the problems of data analysis, optimization of the configuration of the spacecraft and payload, and optimization of the mission design to solve the problem caused by complexity and to enhance the scientific output. Additionally, a more careful investigation of the levels 1 and 2 data analyses investigating the scientific impacts of the gravitational wave sources is also needed. The key problems of the abovementioned space-borne laser interferometer gravitational wave detection missions are generally discussed. Moreover, a brief history of the space-borne laser interferometer gravitational wave detection missions, including LISA, which is the ESA-NASA joint space-borne gravitational wave antenna; Taiji, which is the space-borne gravitational wave mission proposed by the Chinese Academy of Sciences; and TianQin, which is a geocentric orbit space-borne gravitational wave mission raised by Sun Yat-sen University, is reviewed. Finally, the conclusions and future prospect of the Chinese space laser interferometer gravitational wave detection missions are outlined.
