The paper discusses challenges of innovation management that relate to limitations of the innovation concept to match the vast difference in the organisational and institutional contexts in which the concept is applied. Even though the concept of innovation is no longer restricted to manufacturing firms operating on the market, the concept has not accordingly been developed to match the specificities of the many new contexts of application. The paper particularly focuses on the OECD-definition and discusses its shortcomings on the basis of empirical studies in two sectors that have only recently drawn the attention of innovation research: the operational service sector, and the public sector. It is argued that we need to address fundamental meta-theoretical questions for the concept to be useful to innovation managers. Lastly, it is argued that we need a differentiated, context-specific rather than a generic concept of innovation.