Sustainable innovation is more complex than conventional, market-driven innovation, because companies have to consider a wide range of uncertainties concerned with the environment, society, and economics. This literature review shows that resilience is the prevailing way of thinking in the area of sustainability studies, and the main contribution of resilience to sustainability is how to deal with uncertainties. However, there seems to be a scarcity in the current literature on the conceptualization of resilience in the context of innovation. From the duality view, this paper proposes a new concept of innovation resilience based on two dimensions, stability and adaptability, which contribute to maintaining a high level of innovation efficiency, while at the same time adapting to change. The proposed innovation resilience concept attempts to provide an integration of divergent research streams—innovation management, organizational resilience, and sustainability management theory. We develop a conceptual framework that consists of a set of indicators involving the two dimensions by using multiple case studies, upon which future empirical studies can be based.