Non-technical summary. Transdisciplinary approaches for sustainability brings natural and social science researchers together with non researchers to fill gaps in scientific knowledge and catalyze change. By connecting diverse academic fields and sectors, it addresses complex problems and enables learning for problem solving. However, institutional barriers, funding constraints, time limitations, and evaluation criteria hinder collaborative progress. Our review reveals tensions at institutional and individual levels. Our findings underscore the significance of soft skills in assembling effective transdisciplinary teams. Embracing transdisciplinary science, as suggested by our review, can enhance problem-solving, and foster transformations for sustainability and resilience. Technical summary. Sustainability challenges in the age of the Anthropocene require researchers and practitioners to collaborate across multiple academic disciplines and multiple professions outside of universities. In this paper we draw on theories of institutional logics to explore how those involved in transdisciplinary environmental research and practice draw on particular sets of values and norms but encounter challenges to collaboration. These institutional logics include (among others) seeking societal/environmental impact, commercial objectives, and academic knowledge generation. In this paper we review the growing literature on the research experience of transdisciplinarity in sustainability; discuss the processes of managing such research; and present a framework that outlines the challenges and tensions at each stage of the innovation/research process. We set out an agenda for managing tension that calls for recognizing the challenges, learning how to work with tensions, and building capabilities for future careers involving transdisciplinary research. The paper shows a key competence or skill for transdisciplinarians is the ability to develop complex collaborative relationships for sustainability drawing together different institutional logics, approaches, methods, goals, and values. Social media summary. Transdisciplinary science: bridging disciplines, solving challenges. Soft skills and collaboration key to success.