A fusion power plant can only exist with physics and technology acting in synchrony, over space (angstroms to tens of metres) and time (femtoseconds to decades). Recent experience with the European DEMO programme has shown how important it is to start integration early, yet go deep enough to uncover the integration impact, favourable and unfavourable, of the detailed physical and technological characteristics. There are some initially surprising interactions, for example, the fusion power density links the properties of materials in the components to the approaches to waste and remote maintenance in the context of a rigorous safety and environment regime. In this brief tour of a power plant based on a tokamak we outline the major interfaces between plasma physics and technology and engineering considering examples from the European DEMO (exhaust power handling, tritium management and plasma scenarios) with an eye on other concepts. We see how attempting integrated solutions can lead to discoveries and ways to ease interfaces despite the deep coupling of the many aspects of a tokamak plant. A power plant’s plasma, materials and components will be in new parameter spaces with new mechanisms and combinations; the design will therefore be based to a significant extent on sophisticated physics and engineering models making substantial extrapolations. There are however gaps in understanding as well as data – together these are termed “uncertainties”. Early integration in depth therefore represents a conceptual, intellectual and practical challenge, a challenge sharpened by the time pressure imposed by the global need for low carbon energy supplies such as fusion. There is an opportunity (and need) to use emerging transformational advances in computational algorithms and hardware to integrate and advance, despite the “uncertainties” and limited experimental data. We use examples to explore how an integrated approach has the potential to lead to consistent designs that could also be resilient to the residual uncertainties. The paper may stimulate some new thinking as fusion moves to the design of complete power plants alongside an evolving and maturing research programme.