Liouville quantum gravity (LQG) is a family of random fractal surfaces which were originally introduced in the physics literature as canonical models of random two-dimensional Riemannian manifolds. LQG surfaces are the continuum limits of discrete random surfaces such as random planar maps. I will discuss the definition of random planar maps and Liouville quantum gravity, the sense in which the former converges to the latter, and the motivations for studying these objects, assuming no prior background on the subject. I will also mention several open problems.