Ultracold molecules offer unprecedented opportunities for the controlled interrogation of molecular events, including chemical reactivity in the ultimate quantum regime. The proliferation of methods to create, cool, and confine them has allowed the investigation of a diverse array of molecular systems and chemical reactions at temperatures where only a single partial wave contributes. Here we present a brief account of recent progress on the experimental and theoretical fronts on cold and ultracold molecules and the opportunities and challenges they provide for a fundamental understanding of bimolecular chemical reaction dynamics.