The term ‘innovation capability’ has been used recurrently in the innovation literature, but there is still considerable divergence about its meaning and implication to organizations. A consensus exists that, to innovate, organizations must possess innovation capability, and that the ownership of this feature is not a binary process, but rather an evolutionary level process. This evolutionary logic is analogous to the basic structure of organizational maturity models. However, the literature integrating innovation capability into a maturity perspective is still limited. Considering these premises, from a broad bibliographical research, this article presents a framework of reference to represent the entire theoretical domain of innovation capability. Its purpose is to classify the main types of models about this construct available in the reference literature. It is organized at increasing levels of complexity, so that each level creates the conceptual conditions for the construction of more comprehensive models. Similar to the main use cases for maturity models, there are three basic levels for the framework: descriptive; comparative; and, finally, prescriptive models of innovation capability. Considering this cumulative framework, the authors argue that, to be fully understood, innovation capability should be studied using the perspective of maturity models.