I will give an introduction to parabolic geometries: these are Cartan geometries modelled on homogeneous spaces of the form $G/P$, where $G$ is a semisimple Lie group and $P$ is a parabolic subgroup. As a main example of a parabolic geometry, I will discuss the geometry of $(2,3,5)$ distributions, which is related to the exceptional simple Lie group $G=G_2$. I will review some history, explain some of the key methods, and discuss recent developments in the field.