People are fleeing largely from Syria, but also from other countries like Pakistan for instance. Some of them are in poverty, devastated by war and they see the risk of escalation of the civil war. Others are in much better economic shape and they find that it is a time when Europe is likely to accept them. The problem is that Europe was completely unprepared for the waves of migrants, but there was nothing unexpected. There were previous signals coming from Africa, and of course the routes through Turkey and Southern Europe have been attractive and proved to be workable before for refugees, as well as for those who financially gain from passing refugees through other territories.
The question is not whether Europe can accept them, but how it can assimilate these very different groups of people. Everyone is now wondering whether this wave is the final one, or whether one should expect more? Here I do not know the answer, but an obvious response would be that everybody in Europe and Russia is interested in ending of the civil war in Syria, because people are suffering. It looks like an endless civil war in a major country of the Middle East with great history, mix of religions, and important potential both economically and strategically.
However, there are other actors who are not interested in ending the war because they pre-paid those who are not winning so far. Some other money intended for the military opposition and Bashar al-Assad has possibly ended up in the hands of the terrorist groups like ISIS. In my view, it is in the common interest of Russia and Europe, as well the United States and Middle Eastern players to reduce the violence in Syria, addressing primarily the expanding terrorist threat and later on addressing the civil war itself.