Breakthrough technologies introduce a radically new capability or a drastic performance improvement. However, the existing engineering design literature does not specifically pay attention to them. In this paper, we present a conceptual framework for breakthrough technologies, aiming for a more detailed characterization of breakthrough technologies. First, based on a literature survey, we reflect on the relationship between breakthrough technology and innovation. In addition, we explore the relationship between breakthrough technologies at the component and system level. Next, we propose a conceptual framework with dimensions in which breakthroughs may occur and the corresponding expansion of concepts and knowledge, drawing from C-K theory. We subsequently apply the framework to the case of a laser sail-propelled interstellar probe. We conclude that the relationship between component and system-level breakthrough technologies requires further exploration. Furthermore, the coupling between the breakthrough technology and market breakthrough in the form of a new business model seems interesting for future work.