Why are cold molecules so hot?

Herein, we aim to show why the work on translationally (and otherwise) cold molecules has sparked so much inspiration--and anticipation--in both the physics and chemistry communities. We begin by discussing the basic features of cold molecules as implied by their de Broglie wavelengths, large compared with molecular dimensions. We juxtapose cold molecule and cold atom research and recount the challenges that had to be met if molecules were to be cooled and trapped. Subsequently, both the indirect and direct techniques of producing cold and slow molecules are described in some detail, and their applicability to various classes of molecules is discussed. Advanced techniques of manipulating cold or slow molecules are illustrated by the examples of DC and AC trapping and storage. Finally, ongoing and future work with cold and/or trapped molecules is outlined. This includes precision spectroscopy, chemical reaction dynamics, simulations of few- and many-body physics, quantum computing, and tests of fundamental physics.