With the development of parallel robot technology, the necessity of studying the workspace and singularity of parallel robot is presented to improve the motion performance. The research status and characteristics of workspace and singularity at home and abroad are described in detail based on different research methods. Furthermore, individual innovative ideas and common problems for different research methods of workspace and singularity are pointed out. Through deeply analyzing the principle of research methods, the breakthrough is found to solve common problems. Meanwhile, the remaining problems in research are analyzed. Combining with the future development trend, breakthroughs in structural synthesis and theoretical innovation can provide strong impetus for the development of parallel robot. The conclusions and prospects provide valuable references for researchers engaged in this field.