Marstrand in 1964 proved one of the fundamental results in Geometric Measure Theory, relating measure theoretic densities to the geometric structure of a measure. We will discuss recent developments related to Marstrand's density theorem. In particular we establish Marstrand's theorem in the Heisenberg group, relying on an analysis of uniformly distributed measures . We provide a number of examples of such measures,illustrating both the similarities and the differences of this sub-Riemannian setting from its Euclidean counterpart. Based on joint work with J. T. Tyson.