Many-objective optimization has been gaining increasing attention in the evolutionary multiobjective optimization community, and various approaches have been developed to solve many-objective problems in recent years. However, the existing empirically comparative studies are often restricted to only a few approaches on a handful of test problems. This paper provides a systematic comparison of eight representative approaches from the six angles to solve many-objective problems. The compared approaches are tested on four groups of well-defined continuous and combinatorial test functions, by three performance metrics as well as a visual observation in the decision space. We conclude that none of the approaches has a clear advantage over the others, although some of them are competitive on most of the problems. In addition, different search abilities of these approaches on the problems with different characteristics suggest a careful choice of approaches for solving a many-objective problem in hand.