Step dance is the generic term for dance styles where the footwork is the most important part of the dance. Limb movements and styling are either restricted or considered irrelevant.
Step dance is one end of a spectrum of dance styles.
The opposite extreme is Formation dances (e.g. Square dance), where the movement patterns around the dance floor and arm-work are the most important factors (footwork is very simple).
Most social dances fall between these two extremes.
There are very few pure step dances, as most include at least some upper body or arm styling. Often step dances performed in shows add elements of show styling, which can bring them into conflict with the traditionalists.
Tap dancing is probably the most popular form of step dancing taking its influence from a variety of older step-forms.
There are many regionally/country specific types of Step Dance it is considered to be an especially predominant folk dance form in Great Britain and Ireland. Irish hard-shoe dance as popularized by River Dance is a form of step dance and the older Sean-nos is less formal Irish step dance style.
England also has at least two distinguishable forms of step-dance clog done in wooden soled shoes and step-dancing decreasingly tap shoes. Scotland and Wales also have a distinct step-dance traditions.
Other specific styles of step-dancing can be found in the USA, where it can be called clogging or flat-footing and in Canada with the Cape Breton style of dance.
Step-dancing can also be found in other countries such as Malambo from Argentina and Zapateado from Mexico.
Another form of step dancing, Stepping, has been popularized by National Pan-Hellenic Council. This step dance has African roots and is an African American tradition as well as part of Black History. The members of the fraternities and sororities join in steps -- elaborate synchronized group routines that are performed in competitions between the fraternities and sororities called "step shows." Step shows incorporate cheerleading, military, and drill-team moves, especially the call-and-response element inherent in those forms. These aspects are not only important to the energy of stepping for entertainment use but also for bonding and pride within their organizations.
Step dancing is also used with Drum and Bass music.