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Recently Huang, Lutwak, Yang and Zhang introduced a broad class of geometric measures related to convex bodies. Among these are the dual curvature measures ${\widetilde C}_q(K,\cdot)$ of an $n$-dimensional convex body $K$ and $q\in\R$. They are the counterparts to the classical curvature measures of convex bodies in the dual Brunn-Minkowski theory. Here we discuss the associated dual Minkowski problem and present tight subspace concentration inequalities for the dual curvature measures of origin-symmetric convex body for q ≥ n + 1. This supplements former results obtained in the range q ≤ n. Based on a joint work with Hannes Pollehn.