The Muslim attack on Christendom and the resulting conflict, which arose more from their resemblances than from their differences, has gone through three phases. The first dates from the very beginning of Islam, when the new faith spilled out of the Arabian Peninsula, where it was born, into the Middle East and beyond. It was then that they conquered Syria, Palestine, Egypt, and North Africa--all at that time part of the Christian world--and went beyond into Europe, conquering a sizable part of southwestern Europe, including Spain, Portugal, and southern Italy, all of which became part of the Islamic world, and even crossing the Pyrenees into France and occupying for a while parts of France.
After a long and bitter struggle, the Christians managed to retake part but not all of the territory they had lost. They succeeded in Europe, and in a sense Europe was defined by the limits of that success. They failed to retake North Africa or the Middle East, which were lost to Christendom. Notably, they failed to recapture the Holy Land, in the series of campaigns known as the Crusades.
That was not the end of the matter. In the meantime the Islamic world, having failed the first time, was bracing for the second attack, this time conducted not by Arabs and Moors but by Turks and Tartars. In the mid-thirteenth century the Mongol conquerors of Russia were converted to Islam. The Turks, who had already conquered Anatolia, advanced into Europe and in 1453 they captured the ancient Christian citadel of Constantinople. They conquered a large part of the Balkans, and for a while ruled half of Hungary. Twice they reached as far as Vienna, to which they laid siege in 1529 and again in 1683. Barbary corsairs from North Africa--well-known to historians of the United States--were raiding Western Europe. They went to Iceland--the uttermost limit--and to several places in Western Europe, including notably a raid on Baltimore (the original one, in Ireland) in 1631. In a contemporary document, we have a list of 107 captives who were taken from Baltimore to Algiers, including a man called Cheney.
Again, Europe counterattacked, this time more successfully and more rapidly. They succeeded in recovering Russia and the Balkan Peninsula, and in advancing further into the Islamic lands, chasing their former rulers whence they had come. For this phase of European counterattack, a new term was invented: imperialism. When the peoples of Asia and Africa invaded Europe, this was not imperialism. When Europe attacked Asia and Africa, it was.