Protein complexes perform diverse biological functions, and obtaining their three-dimensional structure is critical to understanding and grasping their functions. In many cases, it's not just two proteins interacting to form a dimer; instead, multiple proteins interact to form a multimer. Experimentally resolving protein complex structures can be quite challenging. Recently, there have been efforts and methods that build upon prior predictions of dimer structures to attempt to predict multimer structures. However, in comparison to monomeric protein structure prediction, the accuracy of protein complex structure prediction remains relatively low. This paper provides an overview of recent advancements in efficient computational models for predicting protein complex structures. We introduce protein-protein docking methods in detail and summarize their main ideas, applicable modes, and related information. To enhance prediction accuracy, other critical protein-related information is also integrated, such as predicting interchain residue contact, utilizing experimental data like cryo-EM experiments, and considering protein interactions and non-interactions. In addition, we comprehensively reviewcomputational approaches for end-to-end prediction ofprotein complex structuresbased on artificial intelligence (AI) technologyand describe commonly used datasets and representative evaluation metrics in protein complexes. Finally, we analyze the formidable challenges faced in current protein complex structure prediction tasks, including the structure prediction of heteromeric complex, disordered regions in complex, antibody-antigen complex, and RNA-related complex, as well as the evaluation metrics for complex assessment. We hope that this work will provide comprehensive knowledge of complex structure predictions to contribute to future advanced predictions.