Michael Temkin of the Institute for Advanced Study gives this Members' Colloquium talk on resolution of singularities in algebraic geometry. He traces the field from Hironaka's 1964 proof in characteristic zero through four decades of work to simplify the algorithm and establish its functoriality, then turns to the last decade's discoveries of analogues in logarithmic, relative, stack theoretic, and foliated settings. The core of the lecture is the classical resolution algorithm alongside the so called dream algorithm, found independently in 2019 by Abramovich-Temkin-Wlodarczyk and by McQuillan, which uses weighted stack theoretic blowings up to improve singularities at each step. Time permitting, Temkin extends the discussion to resolution of varieties equipped with a foliation, work with Abramovich, Belotto, and Wlodarczyk. The talk assumes graduate level familiarity with algebraic geometry and is aimed at mathematicians tracking recent progress on a problem long considered essentially settled in its classical form.