Canonical software and systems modelling regards only models that conform to modelling languages and that are created in modelling tools. In practice, these models are often supplemented with free-form activities such as sketching and informal diagramming. Flexible modelling has been proposed to benefit from the combination of free-form activities, from relaxed to no conformance to modelling languages, and canonical modelling with more or less strict conformance of diagrammatic elements to modelling languages. Various tools and approaches have proposed mechanisms to support flexible modelling. In this paper, we report on a systematic literature review of these tools and approaches. We present an analysis of the existing body of knowledge in this area and discuss open research challenges that can help the modelling community identify promising next steps in this area.