It is a rotary dance where the dancers are constantly turning either toward the leader's right (natural) or toward the leader's left (reverse), interspersed with non-rotating change steps to switch between the direction of rotation.
While the slow waltz (Germany) is danced at approximately 90 beats per minute with 3 beats to the bar the Viennese waltz is danced at about 180 beats per minute.
It gained ground through the Congress of Vienna at the beginning of the 19th century and by the famous compositions by Josef Lanner, Johann Strauss I and his son, Johann Strauss II.