Power electronic devices are of great importance in modern society. After decades of development, Si power devices have approached their material limits with only incremental improvements and large conversion losses. As the demand for electronic components with high efficiency dramatically increasing, new materials are needed for power device fabrication. Beta-phase gallium oxide, an ultra-wide bandgap semiconductor, has been considered as a promising candidate, and various β-Ga2O3 power devices with high breakdown voltages have been demonstrated. However, the realization of enhancement-mode (E-mode) β-Ga2O3 field-effect transistors (FETs) is still challenging, which is a critical problem for a myriad of power electronic applications. Recently, researchers have made some progress on E-mode β-Ga2O3 FETs via various methods, and several novel structures have been fabricated. This article gives a review of the material growth, devices and properties of these E-mode β-Ga2O3 FETs. The key challenges and future directions in E-mode β-Ga2O3 FETs are also discussed.