  This paper offers a brief introduction to the framework of "general
probabilistic theories", otherwise known as the "convex-operational" approach
the foundations of quantum mechanics. Broadly speaking, the goal of research in
this vein is to locate quantum mechanics within a very much more general, but
conceptually very straightforward, generalization of classical probability
theory. The hope is that, by viewing quantum mechanics "from the outside", we
may be able better to understand it. We illustrate several respects in which
this has proved to be the case, reviewing work on cloning and broadcasting,
teleportation and entanglement swapping, key distribution, and ensemble
steering in this general framework. We also discuss a recent derivation of the
Jordan-algebraic structure of finite-dimensional quantum theory from
operationally reasonable postulates.
