It's been happening a long, long time and will continue to happen for a long time after we are gone BUT there is one change that might be a gamechanger happening. Many centuries ago Muslims actually conquered what is now Europe but they ruled it in such a way that kept Christians down. That, in turn, led to an uprise in violence by Christians towards Muslims and the crusades began to remove the Muslims from Europe.
Fast forward to today and Muslims are returning in droves in what is said to be a more tolerant society, but the killings continue. The game changer however is birth rate. Muslims have a much higher birth rate than Christians and, a few generations from now, will be the majority in many areas. That means Sharia law and it means more persecution of Christians and Jews. Current politicians in the U.K. are weak and continue to try to create a truly multi-cultural society but it's not working. If you look at a demographics map the Christians, Jews and Muslims often create neighborhoods where they are a majority. In other words even when all in the same country they aren't mixing well.
This will not end for centuries, or longer. Even if Muslims achieve global dominance they will eventually in-fight, become passive and Christians or Jews will reclaim land and expand. It just never ends.