Designing problems are ubiquitous in science research and industry applications. In recent years, Bayesian optimization, which acts as a very effective global optimization algorithm, has been widely applied in designing problems. By structuring the probabilistic surrogate model and the acquisition function appropriately, Bayesian optimization framework can guarantee to obtain the optimal solution under a few numbers of function evaluations, thus it is very suitable to solve the extremely complex optimization problems in which their objective functions could not be expressed, or the functions are non-convex, multimodal and computational expensive. This paper provides a detailed analysis on Bayesian optimization in methodology and application areas, and discusses its research status and the problems in future researches. This work is hopefully beneficial to the researchers from the related communities.