Alexandrite crystal is an excellent broadband tunable laser gain medium with long fluorescence lifetime， high saturation energy density， wide absorption bandwidth and excellent thermo-mechanical properties. In addition to the flash lamp pumping， a variety of visible light sources can also be used as the pumping source such as blue laser diodes， red laser diodes， green lasers， yellow lasers， etc. With the maturity and commercial application of laser diode technology， the alexandrite lasers pumped by red laser diodes have become a hot topic in the field of solid-state lasers. The characteristics of alexandrite crystal are firstly introduced. The domestic and international research progress of alexandrite lasers pumped by flash lamp， laser diodes， etc. are summarized， including continuous， Q-switched， mode-locked and ultraviolet lasers. Finally， the recent advances in their applications to dermatology， lidar， microscope， etc. are introducted and the future developments of alexandrite solid-state lasers are prospected.