The modern computer is a hierarchically organized system of computational artefacts. Inventing, understanding, and applying rules and principles of hierarchy is a subdiscipline of computer science. ‘Computational artefacts’ explains the concepts of compositional hierarchy, the abstraction/refinement principle, and hierarchy by construction. There are three classes of computational artefacts—abstract, material, and liminal. An important example of an abstract artefact is the Turing machine. Sciences involving artefacts are sciences of the artificial, entailing the study of the relationship between means and ends. The ‘science’ in computer science is, thus, a science of means and ends. It asks: how can a computational artefact demonstrably achieve a given human need, goal, or purpose?