Apparatus for indexing glassware through a series of angularly spaced stations includes first and second arrays of glassware gripping fingers mounted on associated carriers that are rotatable about a common axis, both conjointly and with respect to each other. Each carrier is connected to as associated servo motor, which in turn are connected to a controller for rotating the carriers with respect to each other to grip and release glassware between the fingers, and to rotate the carriers conjointly to index the glassware between apparatus stations. One array of glassware gripping fingers includes coil springs for biasing the fingers toward the fingers of the opposing array for accommodating tolerance variations in the glassware. Drive rollers are located at at least some of the stations, and are pivotal into and out of positions for rotating the containers about their axes for inspection or other purposes.