Laser cooling and trapping have revolutionized atomic physics, enabling a wide range of advances in science and technology. In recent years, it has become clear that general methods to produce ultracold molecules would have a similarly broad scientific impact. The rich internal structures of molecules make them versatile tools for a variety of experiments in ultracold chemistry, precision measurement and quantum simulation. However, this same structure poses challenges once believed to be fatal to any attempt at laser cooling. Over the past several years, several groups have devised and implemented methods to overcome these difficulties. Now the standard tools of atomic laser cooling-- including magneto-optical trapping --can work with specific molecular species in a manner similar to the familiar cases for atoms. In this talk, I will review progress in this emerging field and present our experimental effort designed to laser-cool new molecular species with favorable properties for both laser cooling and a range of proposed applications.