Atomic physicists have steadily improved their ability to cool atoms to temperatures where quantum effects reign, and in the past decade they have also trapped loosely bound pairs of atoms. But only in 2008 did they produce large numbers of ultracold pairs that were bound strongly enough to properly be called molecules. Each of these molecules is in its lowest possible state of vibration and rotation, and their overall motion corresponds to temperatures under a millionth of a degree above absolute zero. Bose-Einstein condensation of ultracold atoms 14 years ago spawned a continuing flurry of physics experiments and garnered a Nobel Prize, but researchers expect even richer quantum behavior from ultracold molecules. Understanding how ultracold molecules interact is critical to the experiments.