Observations of multiple-image gravitational lens systems suggest that the projected mass distributions of galaxy haloes may contain substantial inhomogeneities. The fraction of the halo mass in dense substructure is still highly uncertain, but could be as large as a few percent. While halo substructure is seen in numerical simulations of CDM haloes, little of this substructure survives in the innermost regions of haloes, and thus the observational claims for substructure at small projected radii are slightly surprising. There is evidence, however, that even the highest-resolution simulations published to-date are still limited by numerical effects that heat and disrupt substructure artificially in high-density regions. By comparing numerical and semi-analytic (SA) models of halo substructure, we show that current simulations probably underestimate the mass fraction in substructure at small projected radii, by a factor of at least 2–3. We discuss the prospects for using lensing observations as a fundamental test of the nature of dark matter.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html