In recent years, many-objective optimization has gradually become one of the research hotspots of multi-objective optimization. Due to the high-dimensional objective space is difficult to optimize, the research on many-objective optimization problems(MaOPs) is quite challenging and has received extensive attention. The existing surveys usually only focus on a specific aspect and lacks systematic investigation. Therefore, this paper firstly starts from the problem definition, considers the category of MaOPs, and makes the concept analysis of MaOPs. Secondly, the progress of MaOPs is systematically analyzed and some classical methods are introduced by collating the relevant works in recent years. Through the explanation of benchmark functions and performance indicators, the research method of many-objective optimization is comprehensively discussed. Then, five typical many-objective evolutionary algorithms (MaOEAs) are selected. The simulation experiments are carried out on two groups of benchmark functions and four practical problems. The different algorithms are analyzed theoretically by performance indicators and nonparametric tests. Finally, the future research work is prospected based on identifying some frontier problems in many-objective optimization.