Abstract: I explain how to compute explicitly the local cohomology modules supported at determinantal varieties of generic, symmetric, or skew-symmetric matrices, expressing them as direct sums of indecomposable D-modules. A key ingredient is the quiver-theoretic description of the category of equivariant D-modules. In particular, we determine the Lyubeznik numbers of determinantal rings, thus answering a question of Hochster. This is joint work with Claudiu Raicu.