The application of robots in mechanical assembly increases the efficiency of industrial production. With the requirements of flexible manufacturing , it has become a research hotspot to accomplish diversified assembly operations safely and efficiently in unstructured environments. In recent years, many advanced robot assembly strategies have been proposed. Fault monitoring and strategy performance evaluation have also attracted more attention. To promote the development of robotic assembly , this paper systematically reviews the recent research in this field. According to the assembly process, the review separates the research contents into target recognition and searching, compliant strategies for fine insertion motion and fault monitoring. The characteristics of each method are summarized. Furthermore, a performance evaluation for assembly strategies is proposed with typical metrics. We surveyed the classical benchmarks to provide support for standardized performance evaluation. Finally, the challenges and potential directions are discussed.