Mutualist interactions are thought to be ubiquitous, spanning all levels of biological organisation, and involving most species on Earth. However, in contrast to population interactions such as competition and predation, a comprehensive and succinct theoretical explanation of mutualism has proved elusive. We use a new modelling framework that represents obligation, mutualist benefits and mutualist costs in an extended consumer resource approach to develop simple, consistent models of mutualism. We show how populations may stably transition between facultative and obligate mutualism and demonstrate that our solutions do not depend on saturating functions. We show facultative and obligate mutualisms between autotrophs and heterotrophs.