Conventional multi-objective optimization algorithms (MOEAs) with or without preferences are successful in solving multi-and many-objective optimization problems. However, a strong hypothesis underlying their performance is that MOEAs are able to find a representative solution set to cover the entire Pareto optimal front (PF) and decision makers are able to conveniently and precisely articulate their preference, which is not always easy to fulfill in practice. Accordingly, it is suggested that representative solutions in the naturally interesting regions of the PF rather than the whole PF should be targeted. A large body of research has been proposed to search or identify the knees or knee regions over the past decades. Therefore, this paper aims to provide a comprehensive survey of the research on knee-oriented optimization. We start with a discussion of the importance and basic concepts of the knees, followed by a summary of knee-oriented benchmarks and indicators. After that, knee-oriented frameworks and techniques, and real-world applications are presented. Finally, potential challenges are pointed out and a few promising future lines of research are suggested. The survey offers a new perspective to develop MOEAs for solving multi-and many-objective optimization problems.