The BGG resolution, introduced in a seminal paper by Bernstein-Gelfand-Gelfand, and generalised by Lepowsky, is an important device in the representation theory of semi-simple Lie algebras. Its differential-geometric interpretation provides a supply of invariant differential operators between certain natural vector bundles on generalised flag manifolds. The work of Baston and Čap-Slovák-Souček leads to analogues of these operators for parabolic Cartan geometries, with a very direct construction due to Calderbank-Diemer. I will give an example-based introduction to these ideas.