Sub-Riemannian (sR) geometry is the geometry of bracket-generating metric distributions on a manifold. Peculiar phenomena in sR geometry include the exotic Hausdorff dimension describing the growth rate of the volumes of geodesic balls. As well as abnormal geodesics that do not satisfy any variational equation. In this talk I will survey my results, to appear in a forthcoming book, which show how both these phenomena are reflected in the spectral theory of the hypoelliptic Laplacian in sR geometry.