In the last 20 years, evolutionary algorithms (EAs) have shown to be an effective method to solve multiobjective optimization problems (MOPs). Due to their population-based nature, multiobjective EAs (MOEAs) are able to generate a set of tradeoff solutions (called nondominated solutions) in a single algorithmic execution instead of having to perform a series of independent executions, as normally done with mathematical programming techniques. Additionally, MOEAs can be successfully applied to problems with difficult features such as multifrontality, discontinuity and disjoint feasible regions, among others. On the other hand, coevolutionary algorithms (CAs) are extensions of traditional EAs which have become subject of numerous studies in the last few years, particularly for dealing with large-scale global optimization problems. CAs have also been applied to the solution of MOPs, motivating the development of new algorithmic and analytical formulations that have advanced the state-of-the-art in CAs research, while simultaneously opening a new research path within MOEAs. This paper presents a critical review of the most representative coevolutionary MOEAs (CMOEAs) that have been reported in the specialized literature. This survey includes a taxonomy of approaches together with a brief description of their main features. In the final part of this paper, we also identify what we believe to be promising areas of future research in the field of CMOEAs.