There have indeed many twists and turns in the historical clash between the East and the West. All along the borders between the two cultures there was almost always wars - pushing of the envelope, so to speak.
Spain is a classic example with the expulsion of Jews and Moslems in 1492 when Isabella (she got the idea from her personal confessor) that in order to make Spain more pure everyone who wasn't Catholic had to convert or leave. Up until then the three religions had pretty much (not entirely, but pretty much) lived in peace. Portugal soon followed Spain's lead. The Islamic Moors were pushed back to North Africa - from which they had originally conquered Spain.
Another point of contact was in Eastern Europe just east of Vienna - but all through those countries there was an ebb and flow of the 'battle of ideas.' We still see that clash in the recent problems in Kosovo and its religious underpinnings.
The Battle of Lepanto was an epic, a real turning point of history, a battle for the Western Mediterranean - you can read about it here:
Lepanto(by the way, Cervantes was in that battle)
There was also Islamic expansion through what is now Georgia, Azerbajan, and most of the other 'stans.' There is a large Moslem population there now. Islam at one time was going up the Volga delta and there was a group of people there, the Kaspars (where we get the name Caspian Sea) that were so afraid of both the Christians in the West and the Moslems in the East that they chose to convert to Judiasiam.
Islam also expanded into India - that's how modern Pakistan and Bangladesh came into being after the end of the British Raj.
Then, of course, even earlier were the Crusades. But the Crusades were in themselves a Western response (albeit framed in religious terms) to military movement coming from the East. Islam from the beginning was a religion on the move - as Christianity was. Neither was passive.
I believe that one of the things that helped Christianity and its view of itself was the Reformation and the Counter Reformation. It made Christianity able to endure change - to accept that others were not always a threat. It took a while but Christianity was able to modernize itself and adapt. Islam, to my knowledge, has never had a Reformation.