BGG complexes are projective resolutions of certain representations of a Lie algebra. Within the context of Cartan and in particular parabolic geometry they have a nice interpretation in terms of sequences of invariant differential operators. In the first part of this talk we plan to give a brief pedagogical introduction to this subject. We will then focus on the special case of metric projective geometry that is the interaction of projective and pseudo-Riemannian geometry. We show that the BGG machinery of projective geometry combines with structures known as Yang-Mills detour complexes to produce a general tool for generating certain invariant pseudo-Riemannian gauge theories.