The silicon-based on-chip power splitter, an important component of the photonic integrated circuits, has much wider scope of applications such as feedback circuits, tap-port power monitoring, and optical quantization. The design methods of the nanophotonic devices can be roughly divided into the forward design and inverse design methods. This review article outlines the differences and connections between the forward design and inverse design methods, and classifies the inverse design algorithms. In addition, the review article summarizes the representative inverse-designed silicon-based on-chip power splitters in recent years, including multichannel power splitters, arbitrary-split-ratio power splitters, multimode power splitters, broadband power splitters, and multifunction power splitters. Finally, the summary and outlook are made on the development trend of the inverse design algorithms and the inverse-designed power splitters.