Bayesian optimization is a technique for optimizing black-box functions. Due to its high sample utilization efficiency, it is widely applied across various scientific and engineering fields, such as hyperparameters tuning of deep models, compound design, drug development, and material design. However, the performance of Bayesian optimization significantly deteriorates when the input space is of high dimensionality. To overcome this limitation, numerous studies carry out high-dimensional extensions on Bayesian optimization methods. To deeply analyze research methods of high-dimensional Bayesian optimization, this study categorizes these methods into three types based on assumptions and characteristics of different kinds of work: methods based on the effective low-dimensional hypothesis, methods based on additive assumptions, and methods based on local search. Then, this study elaborates on and analyzes these methods. This study first focuses on analyzing the research progress of these three types of methods. Then, the advantages and disadvantages of each method in the application of Bayesian optimization are compared. Finally, the main research trends in high-dimensional Bayesian optimization at the current stage are summarized, and future development directions are discussed.