Rare event detection is a frontier subject in particle physics and nuclear physics. In particular, dark matter detection, neutrino-free double beta decay and neutrino-nucleon coherent elastic scattering have been studied and searched extensively. Rare event detection requires the excellent performance of detectors and extremely low environmental background, so the selection of detectors and related materials is an important issue in rare event detection. Liquid argon has become an important scintillator material for scintillator detectors because of its low cost, good scintillation performance and large volume. Liquid argon was first studied in the 1940s as a sensitive material for ionizing radiation detectors. The first measurements of high-energy beta particles were made using a liquid argon ionization chamber in 1953. ICARUS group put forward the idea of constructing liquid argon temporal projection chamber, and began to make attempts to construct liquid argon temporal projection chamber in 1977. scintillation light signals were collected for the first time in a liquid argon temporal projection chamber in 1999. Thus, the drift time of the particle can be obtained to determine the particle track. After development, single-phase liquid argon scintillator detector and two-phase argon time projection chamber have become two common types of liquid argon detectors, and have been used in rare event detection experiments by domestic and foreign experimental groups in recent years. For dark matter detection, the DEAP group and DarkSide group have achieved good results with single-phase liquid argon scintillation detector and two-phase argon time projection chamber, respectively. For neutrino-free double beta decay experiments, GERDA group has done a lot of research on liquid argon anti-coincidence system and applied it to experiments. The LEGEND group, which is the combination of GERDA and MAJORANA experimental group, upgraded the liquid argon anti-coincidence system which was applied in the following LEGEND-200 project. For neutrino-nucleon elastic scattering experiments, COHERENT obtained the latest results using liquid argon detectors. The Taishan neutrino-nucleon coherent elastic scattering project of the High Energy Institute of Chinese Academy of Sciences has also begun to study the feasibility of liquid argon anti-coincidence system. Finally, this paper discusses the direction of optimization of liquid argon detector, such as exposure, background level and optical readout scheme, and gives a good prospect of liquid argon detector in rare event detection in the future.