Garnet crystals possess many properties that are desirable in laser host materials, e.g., they are suitable for diode laser (LD) pumping, stable, hard, optically isotropic, and have good thermal conductivity, permitting laser operation at high average power levels. Recently, a new garnet material, GYSGG, was developed by replacing some of the yttrium ions (Y3+) with gadolinium ions (Gd3+) in YSGG, demonstrating great potential as a laser host material. GYSGG crystals doped with trivalent neodymium ion (Nd3+) and erbium ions (Er3+) were successfully grown for laser generation in the near- and mid-infrared range, with some of the laser performances reaching the level of mature laser gain media. This paper gives an overview of the achievements made in Nd3+- and Er3+-doped GYSGG lasers at different wavelength ranges. Additionally, full descriptions on Q-switching, mode-locking and wavelength-selecting methods for Nd:GYSGG, and the mechanisms of power scaling by co-doping sensitizers and deactivators in Er:GYSGG, are given. It is expected that this review will help researchers from related areas to quickly gain an understanding of these laser materials and promotes their commercialization and applications.