Abstract: Liouville quantum gravity (LQG) is a natural model for a random surface with origin in the physics literature. A very powerful tool in the study of LQG is conformal welding, where multiple LQG surfaces are combined into a single LQG surface. The interfaces between the original LQG surfaces are typically described by variants of the random fractal curves known as Schramm-Loewner evolutions (SLE). We will give an introduction to LQG and SLE, along with an overview of recent and classical conformal welding results and some of their applications.