Consider the set of labelled trees on n vertices. Cayley’s formula tells us that there are n^{n-2} elements in this set; pick one uniformly at random. What can we say about this random tree in the limit as n goes to infinity? There are several different ways in which this (very vague!) question may be approached. One is via a scaling limit, that is, finding a good way to rescale the object with n (in this case, by giving each of its edges length n^{-1/2}) and then sending n to infinity, so that we obtain a continuum limit which is a random tree-like object. The limit in this case was discovered by David Aldous in 1990, and is known as the Brownian continuum random tree. My aim in this talk is to give an introduction to this beautiful area of probability theory.