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 are being planned and implemented gradually. Rare event detection requires not only the detectors to possess excellent performances but also 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 obtained by using a liquid argon ionization chamber in 1953. The ICARUS group put forward the idea of constructing liquid argon temporal projection chamber, and made attempt to construct liquid argon temporal projection chamber in 1977. The 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 extensively used in rare event detection experiments 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, the GERDA group has done a lot of researches of liquid argon anti-coincidence system and applied the said system 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 to the following LEGEND-200 project. For neutrino-nucleon elastic scattering experiments, COHERENT obtained the latest results by using the 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 optimizing the liquid argon detector, such as exposure, background level and optical readout scheme, and gives a good prospect of liquid argon detector applied to rare event detection in the future.