In this Chapter we will discuss modelling and reductionism in science and engineering, and how this relates to the new idea of digital twins. In particular, we focus on the historical context of modelling and reductionism for dynamics and control of engineering systems. Both active and passive control methods will be discussed, including the novel ideas associated with the inerter. Based on a selected review of the philosophy of modelling, we consider the role of knowledge and complexity in model making. The related topics of systems engineering, uncertainty analysis and artificial intelligence are also briefly discussed in the context of digital twins. We will argue that utility, trust and insight are the three key properties of models that will ideally be extended to digital twins. We then consider how digital twins will require the dynamic assembly of digital objects in order to recreate emergent behaviours. In order to implement a digital twin, an operational platform is required. We briefly present an aircraft example of a digital twin operational platform. Lastly we consider digital twin knowledge models and ontologies, and how this topic might help shape digital twins in the future.