In joint work with Aaron Naber and Daniele Valtorta, we demonstrate a quantitative structure theorem for measures in R^n under assumptions on the Jones beta-numbers, which measure how close the support is to being contained in a subspace. Measures with this property have arisen in several interesting scenarios: in obtaining Hausdorff measure estimates on the singular set of minimal surfaces; in characterizing L2-boundedness of Calderon-Zygmund operators; and as an analyst’s formulation of the traveling salesman problem.