Abstract: We shall present a method for constructing complexes of invariant differential operators on manifolds endowed with various geometric structures. The geometric structures will mainly be certain bracket generating distributions. For these structures the constructed complexes provide fine resolutions of the sheaf of locally constant functions and so can serve as an alternative to the de Rham complex. In the case of parabolic geometries we recover the BGG complexes associated to the trivial representation. Joint work with Robert Bryant, Michael Eastwood and Rod Gover.