A marine autonomous surface vehicle (ASV) is a kind of autonomous marine robot with intelligent and flexible use advantages. They are mainly divided into two categories: unmanned vessels and unmanned sailboats. Marine ASVs are essential in marine science, industry, environmental protection, and national defense. One of the primary challenges faced by marine ASVs is autonomously planning paths in an intricate marine environment. Numerous research findings have surfaced in recent years, including the combination with popular machine learning. However, a systematic literature review is still lacking, primarily a comprehensive comparison of two types of ASV path planning methods. This review first introduces the problem and evaluation indicators of path planning for ASVs. Then, aiming at unmanned vessels and sailboats, respectively, it sorts out various path planning algorithms proposed in the existing literature, including the advantages and limitations of both kinds of ASVs, and discusses them in combination with evaluation indicators. Also, this paper explores how marine environmental factors affect path planning and its corresponding treatment methods. Finally, this review summarizes the challenges of unmanned ship path planning, proposes potential technical solutions and future development directions, and aims to provide references for further development in this field.