Maximum entropy distributions on discrete domains have been studied in a number of contexts over the past few decades. In particular, they have been used in deterministic algorithms for the approximation of the permanent, scaling problems for torus actions, applications of spanning tree sampling problems, and beyond. These applications are intimately linked to distributions on some finite support set, with a given expectation, and which maximize entropy. In this talk, we will discuss the generalization of maximum entropy distributions from finite discrete support sets to continuous manifolds. Such distributions arise in connection to a number of topics; for example, quantum entropy, interior point methods, matrix distributions studied in statistics, the isotropic constant, and low-rank matrix approximation. We will discuss a few of these applications, along with some of the computability issues which arise when moving from discrete support to continuous. We will also briefly discuss the connection between this generalization and the norm minimization techniques used for general scaling problems. This is joint work with Nisheeth Vishnoi.