Molecular Mixology is a special practice of mixing drinks using the analysis and techniques found in science to understand and experiment with cocktail ingredients on the molecular level. Inspired by the practice of molecular gastronomy (which works in similar ways with food dishes) this practice has become a popular study of many mixologists. The purpose is to manipulate states of matter to create new flavors, feels, textures and visuals that enhance the drink and make the drinker's experience more interesting.
Popular techniques of molecular mixology include the use of foams, liquid nitrogen, gels, mists, heat, solidifying liquids, etc. There are many bartenders and establishments throughout the world that feature or specialize in molecular mixology, just as there are restaurants that specialize in molecular gastronomy. However, the practice is sometimes touted as novel, gimmicky and, with the absence of discretion, can be overwhelming for some drinkers.
To give you an idea of molecular mixology, the Small Screen Network has some interesting videos in which Robert Hess (aka Drink Boy) interviews well-known mixologist Jamie Boudreau about some of the finer points of this science.