Empirical models are a way of formalising data that arises in physical experiments. They were first proposed by Abramsky and Brandenburger as part of a framework to analyse fundamentally non-classical phenomena in quantum systems. Conveniently from a computer science perspective, they abstract away from the mathematical baggage of quantum theory and instead allow the key phenomena to be characterised purely as features of empirical data. After introducing the basic framework I will discuss some more recent results and developments, drawing on joint work with a number of collaborators. In particular: quantum computations can simply be modelled as classical computations with the additional ability to interact with a resource empirical model; quantitative measures of non-classicality can be shown to relate directly to some basic quantum-over-classical computational advantages; and the beginnings of a category-theoretic approach to reasoning about empirical models have emerged.