How is scientific knowledge used, adapted, and extended in deriving phenomena and real-world systems? This paper aims at developing a general account of 'applying science' within the exemplar-based framework of Data-Oriented Processing (DOP), which is also known as Exemplar-Based Explanation (EBE). According to the exemplar-based paradigm, phenomena are explained not by deriving them all the way down from theoretical laws and boundary conditions but by modelling them on previously derived phenomena that function as exemplars. To accomplish this, DOP proposes to (...) maintain a corpus of derivation trees of previous phenomena together with a matching algorithm that combines subtrees from the corpus to derive new phenomena. By using a notion of derivational similarity, a new phenomenon can be modelled as closely as possible on previously explained phenomena. I will propose an instantiation of DOP which integrates theoretical and phenomenological modelling and which generalises over various disciplines, from fluid mechanics to language technology. I argue that DOP provides a solution for what I call Kuhn's problem and that it redresses Kitcher's account of explanation. (shrink)