Here are three studies of dark matter ("DM") dominated objects, with the aim of constraining the shapes of the inner regions of their DM halos. The first chapter is an introduction to the dissertation. Using galaxy cluster Abell 611 as a prototype, in Chapters 2 and 3 we model the strong lensing of eight galaxy clusters to infer the mass distribution in the range of 10 kpc to 150 kpc from the centers of the clusters, then subsequently derive constraints on self-interaction cross-section over mass $\sigma/m$ of DM particles. We infer the mass profiles of the central DM halos, bright central galaxies, key member galaxies, and DM subhalos for the member galaxies for all 8 clusters using the QLens code. The inferred DM halo surface densities are fit to a self-interacting dark matter ("SIDM") model, which allows us to constrain the self-interaction cross section over mass $\sigma/m$. When our full method is applied to mock data generated from two clusters in the Illustris-TNG simulation, we find results consistent with no DM self-interactions as expected. For the eight observed clusters with average relative velocities of $1458_{-81}^{+80}$ km/s, we infer $\sigma/m = 0.082_{-0.021}^{+0.027} \rm cm^2/g$ and $\sigma/m < 0.13~ \rm cm^2/g$ at the 95\% confidence level. In Chapter 4 we examine the bright dwarf spheroidal galaxies of the Milky Way, using a novel approach not yet completed in literature on these 9 objects: the use of phase space distribution functions. We use as data the observed surface density, velocity dispersion and fourth-order velocity moment. We use mock data from the Gaia Challenge project to show that the model can infer important characteristics such as $r_{\mathrm{max}}$, $v_{\mathrm{max}}$, the half-light radius, the density at 150 pc and the core radius. We find that the accuracy of the predictions is highest for data sets in which the stellar component is not too deeply embedded within the DM halo. For the observed sample, we infer these same parameters with accuracy comparable to those using a Jeans analysis approach. We confirm the wide diversity of inner densities in these objects, in particular that the Draco, Leo I, Leo II and Ursa Minor dwarf spheroidal galaxies are approximately four times more dense than Carina, Sextans and Fornax.