As a promising ultra-wide bandgap semiconductor, the <italic>& x03B2;</italic>-phase of Ga<sub>2</sub>O<sub>3</sub> has attracted more and more interest in the field of power electronics due to its ultra-wide bandgap (4.8 & x00A0;eV), high theoretical breakdown electric field (8 MV & x002F;cm), and large Baliga & x0027;s figure of merit, which is deemed as a potential candidate for next generation high-power electronics, including diodes, field effect transistors (FETs), etc. In this article, we introduce the basic material properties of Ga<sub>2</sub>O<sub>3</sub>, and review the recent progress and advances of <italic>& x03B2;</italic>-Ga<sub>2</sub>O<sub>3</sub> based metal & x2013;oxide & x2013;semiconductor field-effect transistors (<sc>mosfet</sc>s). Due to the problematic p-type doping technology up to now, the enhancement-mode (E-mode) <italic>& x03B2;</italic>-Ga<sub>2</sub>O<sub>3</sub> FETs face more difficulties, compared with depletion mode (D-mode). This article focuses on reviewing the recent progress of E-mode Ga<sub>2</sub>O<sub>3</sub> <sc>mosfet</sc>s, summarizing and comparing various feasible solutions when p-type doping is absent. Furthermore, the device fabrication and performances of state-of-art <italic>& x03B2;</italic>-Ga<sub>2</sub>O<sub>3</sub> <sc>mosfet</sc>s, including D-mode, E-mode, and planar & x002F;vertical structure are fully discussed and compared, as well as potential solutions to the challenges of Ga<sub>2</sub>O<sub>3</sub> FETs.