Thermodynamics is one of the most effective paradigms in physics, with applications from the tiny scale of molecular engines to the grand scale of stars and black holes. The reason of such effectiveness can be traced back to the fact that thermodynamic approach is, in large part, independent of the physical theory describing the system of interest: no matter whether the system is classical or quantum, relativistic or non-relativistic, the concepts of equilibrium, entropy, and free energy can be successfully employed. But why? Recently, different groups have started to investigate which requirements have to be satisfied in order for a given physical theory to support a sensible thermodynamics. Here I will present our proposal, arguing that the foundations of thermodynamics are to be found in the way physical systems compose with one another. Specifically, I will show that most of the familiar properties of equilibrium states and entropy can be retrieved from the requirement that every physical system can be modeled as part of a larger system in a pure state that evolves reversibly through time. I will argue that classical thermodynamics is no exception to this scheme: while classical probability distributions cannot be reduced to classical pure states, the key point is that classical systems can in principle be composed with other (non-classical) systems and that the resulting composite has the desired properties. This observation leads to the conjecture that the physical theories admitting a sensible thermodynamics are those and only those that admit, in principle, a pure and reversible extension.