Abstract: A set of shapes is called aperiodic if they admit tilings of the plane, but none that have translational symmetry. Starting in the 1960s, progress in our understanding of such tilings produced progressively smaller aperiodic sets, but failed to arrive at a single shape that tiles aperiodically, also known as an aperiodic monotile. In 2023, we resolved that open question by proving that the "hat", a union of eight kites, is an aperiodic monotile. In this talk I provide background on aperiodicity and related topics in tiling theory, review the history of the search for for an aperiodic monotile, and present the new monotiles that we discovered.