Waltz is the oldest ballroom dance, dating from the 18th century. When it was first introduced to ballrooms, it was met with outrage because it was the first dance with the man's arm around the lady's waist.
The first waltz was the Viennese Waltz but later slower waltz music was written that called for long gliding steps in place of the constant turning of the Viennese Waltz.
Both the slower version of Waltz and the Viennese are performed in competition today. The slower waltz is the one that is usually taught for social dancing.
Below, is a video of the Waltz in competition.