The mass profile of galaxies and clusters on small scales is important to a wide variety of problems in astrophysics and cosmology. Gas cooling and stellar feedback directly impact the dark matter distribution, and uncertainty in the stellar initial mass function makes it difficult to separate baryonic and dark components. The abundance of substructure and the inner halo slope are also sensitive to dark matter self-interactions. Uncertainties in these effects will hinder gravitational lensing experiments aiming to constrain dark energy with cluster masses and cosmic shear. I will discuss challenges and opportunities for addressing these issues with weak lensing on small scales. In particular, I will discuss results from a study of halo miscentering with a galaxy group catalog, and forecasts for combining shear and magnification with dynamical masses from current and future surveys. I will also present a novel technique that uses kinematic information from background sources to infer their intrinsic shapes, greatly improving the lensing signal-to-noise per galaxy and enabling weak lensing measurements from individual galaxies.
