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.