Liouville quantum gravity (LQG) is a random surface of fundamental importance in probability theory and mathematical physics. There are, roughly speaking, two approaches to LQG. The first is motivated by the interpretation of LQG as the scaling limit of random planar maps, and studies the interplay between LQG and random fractal curves called Schramm-Loewner evolution. The second focuses on Liouville conformal field theory (LCFT), which is constructed via LQG. This mini course explores the framework developed by the speaker and coauthors which combines the two perspectives to derive exact solvability results for LQG, SLE, and LCFT. In particular, we will discuss some applications to the conformal loop ensemble.