The residual finiteness growth of a finitely generated group quantifies how well approximated the group is by its finite quotients. We give an introduction to quantifying residual finiteness while highlighting a main theme in this area: one can draw group theoretic information of a group from its residual finiteness growth. We survey some recent results in this direction while working out a few examples (including some special linear groups and finitely generated hyperbolic groups). This talk covers joint work with Brandon Seward and Ben McReynolds.