The analytical distinction between critical and problem-solving research is useful. At the onset of research, the latter takes the world as it is while the former questions it. Yet, in striving to integrate social and natural dimensions of sustainability such a distinction may surface as a methodological obstacle. We illustrate how combining critical with problem-solving approaches can help us imagine, understand, and enable transitions to sustainability. First, we trace the historical divide and potential complementarity between critical and problem-solving approaches in the natural and social sciences and how critical approaches in the social sciences are informed by critical theory. Inspired by Robert Cox, we then analyze a set of PhD theses in an interdisciplinary research program engaging in critical and problem-solving research, on and for sustainability. We do so based on Cox's terminology, especially the concepts of ideas, institutions, material capabilities, and frameworks for action, and then show how selected research narratives apply them. To conclude, we emphasize that integrated understandings of human-environmental dynamics are facilitated by multiscalar approaches, theoretical and methodological pluralism, and a combination of natural and social science theory, typical of the interdisciplinary research field of sustainability science. [ABSTRACT FROM AUTHOR]