Manuel Giménez Medina, José González Enríquez
, Francisco José Domínguez Mayo 
Public funding, being the primary source for innovation, imposes restrictions caused by a lack of trust between the roles of public funders and organisations in the innovation process. Capability and maturity innovation assessment models can improve the process by combining both roles to create an agile and trusting environment. This paper aims to provide a current description of the state-of-the-art on capability and maturity innovation assessment models in the context of Information and Communication Technologies. To this end, a Systematic Mapping Study was carried out considering high-quality published research from four relevant digital libraries since 2000. The 78 primary studies analysed show several gaps and challenges. In particular, a common ontology has not been achieved, and Innovation Management Systems are scarcely considered. Concepts such as open innovation have not been correctly applied to incorporate all Quadruple Helix stakeholders, especially the government and its role as a public funder. This implies that no studies explore a standard agile public–private maturity model based on capabilities since the public funders’ restrictions have not been considered. Furthermore, although some concepts of innovation capabilities have evolved, none of the studies analysed offer a comprehensive coverage of capabilities. As potential future lines of research, this paper proposes 11 challenges based on the 5 shortcomings found in the literature.
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