The Wikipedia entry on Cyprus says its location is in Europe.
However,
Perhaps it would be correct to say that based on the strict geographical definition of Europe, Cyprus is not part of Europe; but based on the political notions of Europe, it is?
Cyprus's position:
Geographically it is considered to be in Asia. Here is the map.
Tectonically it is on a small separate plate together with most of Turkey, is separate from the Eurasian plate, and doesn't belong to the African plate. Here is the map.
Politically it is, in some sense, in Europe, since it is a member of the EU. But, for example, in the UN, it is considered to be Asian. It is culturally mostly Greek, but has a very notable and separated Turkish minority in the northeast.
Other: Cyprus used to be a member of the Eurovision song contest, a member of UEFA Europa League, and as an entrant in the Olympic Games, Cyprus (and even Turkey) is categorized as a European country. Here is the color-coded Olympic map.
So I would say that, in the most common terms, Cyprus is considered to be a country located in Europe, but in some perspectives, Asia, or between Europe and Asia.
In terms of the EU, yes, it joined the EU in 2004 http://europa.eu/about-eu/countries/index_en.htm
Geographically, it lies on the edge of the Anatolian and African continental plates.
Cyprus is geographically in Asia. It is 70km away from the south eastern coast of Turkey and 100 km away from the coast of Syria. Culturally, Cyprus is Oriental, just like Anatolia and the Balkans. Its cultural heritage is neither European nore Asian. I don't know what European or Asian cultures mean. There is Western culture and Oriental culture. The Balkans are in Europe but have an Oriental culture while U.S.A. is in America and has a Western culture, so Kossovo has culturally more in common with Turkey while U.S.A. has more in common with Great Brittain. Cyprus belonged to the Ottoman Empire till the second half of the XIXth century and before that, to the Crusaders, Byzantine Empire, Persian Empire and Babylonian Empire, just like parts of Africa, Europe and Asia so... Cyprus shares common foods, music styles, dances and other traditions with other countries from the Balkans, the Caucasus, Middle East, North Africa and Anatolia. Politically it is part of Europe. But that doesn't mean much because Israel is part of Eurovision and European Champion's League but that doesn't make it European.
Well culturally Cyprus is like Europe but if you look geologically it is surely in Asia. The border between Asia and Europe is passing through Istanbul in Turkey which is in Europe but the remaining is in Asia. Cyprus is below Turkey so it is surely in Asia. But the people of Cyprus says they are in Europe because it is more developed than Asia.
