Iceland joined the Schengen states on March 25, 2001, an agreement of 26 states to abolish checks at their common borders on the movement of persons and facilitate the transport and movement of goods at those borders.
All persons requiring visas, not holding a valid Schengen visa in their travel document, must apply for a visa at the applicable embassy/consulate before travelling to the Schengen area. Embassies/consulates representing Iceland handle applications, see here.
Visas may be granted for business trips, tourism, private reasons (family and friends), official visits, short term studies and for political, scientific, cultural, sports or religious events.