Breakthrough technologies are technologies that introduce radically new capabilities or a performance increase of at least an order of magnitude. Examples are the turbojet, inertial navigation, and autonomous vehicles. The existing literature on the sociology and history of technology has used numerous case studies of breakthrough technologies for exploring their communities of practice, institutional context, and geographic context. The strategic management literature has dealt with the relationship between breakthrough technologies and a firm’s competitivity. However, the role that models played during the very early phases of the emergence of a potential breakthrough technology does not seem to have been explored yet. This presentation addresses the questions of how engineering models are used in assessing the feasibility of potential breakthrough technologies and what the particular characteristics of the use of engineering models in this context are. The basic problem setting is the relationship between feasibility-related questions about a potential breakthrough technology and models that provide support for answers pertaining to these questions. Important issues regarding this relationship are often about the validity of analogies (If x is feasible in context y, then x is feasible in context z.), scalability (If x works with a set of parameters Y, then it works with a changed set of parameters Y’.), and the unexpected emergence of new physical effects, which I call “technology-dependent physics”. By using four historical examples of (potential) breakthrough technologies and one detailed case study, the role of these three attributes of models is explored. It is concluded that these three attributes seem to play an important role in assessing the feasibility of breakthrough technologies via models, raising the question about what form of validity they would result in.