Empirical research has confirmed that a positive relationship exists between the implementation of innovation activities and the future performance of organizations. Firms utilize resources and capabilities to develop innovations in the form of new products, services or processes. Some firms prove to be better at reproducing innovation success than others, and the capacity to do so is referred to as innovation capability. However, the term innovation capability is ambiguously treated in extant literature. There are several different definitions of the concept and the distinction between innovation capabilities and other types of capabilities, such as dynamic capabilities, is neither explicitly stated, nor is the relationship between the concept and other resource- and capability-based concepts within strategy theory established. Although innovation is increasingly identified as crucial for a firm’s sustainable competitiveness in contemporary volatile and complex markets, the strategy-innovation link is underdeveloped in extant research. To overcome this challenge this paper raises the following research question: What type of innovation capabilities are required to innovate successfully? Due to the status of the extant research, we chose a conceptual research design to answer our research question and the paper contributes with a conceptual framework to discuss what innovation capabilities firms need to reproduce innovation success. Based on careful examination of current literature on innovation capability specifically, and the strategy-innovation link in general, we suggest that innovation capability must be viewed along two dimensions – innovation novelty and market characteristics. This framework enables the identification of four different contexts for innovation capabilities in a two-bytwo matrix. We discuss the types of innovation capabilities necessary within the four different contexts. This novel framework contributes to the understanding of the strategy-innovation link as well as clarifies the conceptual understanding of capabilities within the strategy literature and establishes the relationship between these structures and innovation management theory.