Crops that provide ecosystem services (ESs) beyond crop production are gaining interest from farmers, policymakers, and society at large. Cover crops (CCs), grown either as the sole crop or mixture, provide multiple ESs that contribute to achieving the sustainable development goals (SDGs) of the United Nations. Little is known to date as to whether and to what extent ESs provided by CCs are affected by genotype × environment × management (G×E×M) interactions. Understanding these interactions could help to maximize the ESs of CCs while minimizing their ecosystem disservices. To this end, we highlight existing research gaps in CC research and then propose key research strategies, including the need for a paradigm shift in defining, managing, and utilizing CCs.