The Continuum Random Tree, introduced by Aldous in the 90’s, arises in numerous
different ways, for instance as the scaling limit of large uniform trees, via Brownian excursions, or
via a Poisson point processes. It carries a natural structure as a metric measure space and has
recently featured prominently in the LeGall’s and Miermont’s work on the Brownian map, as well
as Duplantier’s, Miller’s and Sheffield’s Brownian sphere. Beginning from basic definitions, I will
describe some of the highlights of this emerging theory such as connections to Liouville Quantum
Gravity, and will describe how to draw the CRT in the plane in a conformally natural way.