  Fix a manifold M, and let V be an infinite dimensional Lie algebra of vector
fields on M. Assume that V contains a finite dimensional semisimple maximal
subalgebra A, the projective or conformal subalgebra. A projective or conformal
quantization of a V-module of differential operators on M is a decomposition
into irreducible A-modules. We survey recent results on projective
quantizations and their applications to cohomology, geometric equivalences and
symmetries of differential operator modules, and indecomposable modules.
