The waltz is a couple dance in 3/4 time, done primarily in closed position, the commonest basic figure of which is a full turn in two measures using three steps per measure. It first became fashionable in Vienna in about the 1780s, then spread to many other countries within the next few years. The waltz, and especially its closed position, became the example for the creation of many other ballroom dances. Subsequently, new types of waltz have developed, including many folk dance and several ballroom dance types. In contemporary ballroom dance, the fast versions of the waltz are called Viennese Waltz.
The waltz is sometimes assumed to be a descendant of the lavolta. This is unproven, and the fundamental differences in technique make it hard to imagine how the one could be so closely related to the other. The main reason to assume such a descent is merely that these are two of the earliest European turning dances in closed positions for which we have explicit written instructions. It is likely, however, that they could have had a common ancestor.
International Standard Waltz[?] has only closed figures; that is, the couple never leaves closed position. Contrast American-Style Waltz[?], in which some figures involve breaking contact entirely. For example, the Syncopated Side-by-Side with Spin includes a free spin for both the man and lady. Open rolls are another good example of an Open Dance Figure[?], in which the lady alternates between the man's left and right sides, with the man's left or right arm (alone) providing the lead.
A typical Waltz figure (from the man's perspective) starts lowered into the knees and travelling forward with a strong heel lead. Count 2 rises and is taken on the ball of the foot, and count 3 starts on the ball of the foot and lowers to the heel as the couple begins to lower in preparation for the next measure. A smooth rise-and-fall action is a primary characteristic of this dance.
"Waltz" is also the name for the kind of music to which one dances the waltz. In this sense, there are waltzes in nearly every kind of European and Euro-American folk music as well as in classical or "art" music. Many songs, too, are "in waltz time." The music is written out in 3/4 time and typically played at a rather slow tempo (but see above).