What if you could take a handful of simple building blocks — each describing a random time until an event — and combine them into a new random time, without ever leaving the same family of distributions? That is exactly the power of the closure properties of phase‑type distributions. In this chapter we walk through the most useful ways to put phase‑type distributions together and still end up with a phase‑type distribution, and we illustrate the ideas with the classic Erlang distribution.