Characterizations of autism include multiple references to rigid or inflexible features, but the notion of rigidity itself has received little systematic discussion. In this paper we shed some light on the notion of rigidity in autism by identifying different facets of this phenomenon as discussed in the literature, such as fixed interests, insistence on sameness, inflexible adherence to routines, black-and-white mentality, intolerance of uncertainty, ritualized patterns of verbal and non-verbal behavior, literalism, and discomfort with change. Rigidity is typically approached in a disjointed fashion (i.e., facet by facet), although there are recent attempts at providing unifying explanations. Some of these attempts assume that the rigidity facets mainly relate to executive functioning: although such an approach is intuitively persuasive, we argue that there are equally plausible alternative explanations. We conclude by calling for more research on the different facets of rigidity and on how they cluster together in the autistic population, while suggesting some ways in which intervention could benefit from a finer-grained view of rigidity.