Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmological inhomogeneities that can be used to study the effect of inhomogeneities on the universe's expansion. In this thesis, new cosmological black hole solutions are obtained by generalizing the expanding Kerr-Schild cosmological black holes to obtain the charged case, by performing a Kerr-Schild transformation of the Einstein-de Sitter universe (instead of a closed universe) to obtain non-expanding Kerr-Schild cosmological black holes in asymptotically-flat universes, and by performing a conformal transformation on isotropic black hole spacetimes to obtain isotropic cosmological black hole spacetimes. The latter approach is found to produce cosmological black holes with energy-momentum tensors that are physical throughout spacetime, unlike previous solutions for cosmological black holes, which violate the energy conditions in some region of spacetime. In addition, it is demonstrated that radiation-dominated and matter-dominated Einstein-de Sitter universes can be directly matched across a hypersurface of constant time, and this is used to generate the first solutions for primordial black holes that evolve from being in radiation-dominated background universes to matter-dominated background universes. Finally, the Weyl curvature, volume expansion, velocity field, shear, and acceleration are calculated for the cosmological black holes. Since the non-isotropic black holes introduce shear, according to Raychaudhuri's equation they will tend to decrease the volume expansion of the universe. Unlike several studies that have suggested the relativistic backreaction of inhomogeneities would lead to an accelerating expansion of the universe, it is concluded that shear should be the most likely influence of inhomogeneities, so they should most likely decrease the universe's expansion.