A few-mode erbium-doped fiber amplifier (FM-EDFA) is a key device for realizing long-haul and high-capacity mode-division multiplexing (MDM) transmission. However, different mode channels across a wide wavelength band generate both mode-dependent and wavelength-dependent gains, leading to differential mode gain (DMG) over the wavelength span. This severely constrains the capacity enhancement of MDM transmission systems. In this study, we provide a comprehensive review of recent progress in the gain regulation of FM-EDFA. We systematically discuss the generation mechanism of DMG and its optimization strategies. The performance of DMG under various regulation schemes is then presented. Finally, we explore the research challenges related to DMG equalization under conditions of higher mode counts and wavelength-division multiplexing (WDM) transmission.