Three-phase transformerless photovoltaic (PV) inverters are widely used in solar systems due to their advantages, such as relatively low cost, small size, and high performance. However, they encounter leakage current problems, which can lead to issues such as harmonic damage, grid distortion, and safety risks to individuals. Effectively suppressing leakage current is a critical issue that needs to be addressed for transformerless PV inverters. The purpose of this research is to review advancements made in suppressing leakage current over the past few years in the research area of three-phase transformerless photovoltaic inverters. By summarizing recent research, this paper presents several topologies that efficiently eliminate system leakage current. Additionally, this paper analyzes optimal modulation methods for these topologies in detail. Through a comparison of these topologies, this paper offers insights for future photovoltaic system design. Furthermore, this paper suggests methods to effectively suppress leakage current, reduce total harmonic distortion (THD), and improve efficiency. Finally, this paper discusses expectations for future research and development in the photovoltaic industry.