I saw an article yesterday where a church historian suggested that the rise of Islam was the major turning point in church history post AD 70. I think he's right. The Muslims arose, and the Church took actions to defend her holy cities against them. She made alliances with kings for extra strength. Power was centralized between the Holy Roman Empire and the Pope. The Popes began to assert their authority as vicars of Christ. Here is one more influence they had on the medieval church: the Rise of Scholasticism.
Europeans began talking to Arabian scholars during their time of the Crusades. The Arabians had preserved all of the classic Greek literature from Aristotle and Plato. Men like William of Moerbeke and Averroes began translating those works into Latin, and people began reading them. Monks especially loved reading these philosophies. As a result, the Scholastic movement thrived. Universities began, and people began studying theology through logic and reason. They mostly did not let the pagan values influence how they taught the Bible, though that would be a result later on. They still studied the Bible, creeds, and the early church fathers.
Medieval science was different. Instead of finding knowledge by experiments and observation, the inductive method, the Scholastics would use deductive logic chiefly through the syllogism, also a product of Aristotle. An example is: "No reptiles have fur. All snakes are reptiles. No snakes have fur." This logic is how they would figure things out. This revolution led to both good theology and theology reduced only to reason when God is so much beyond our human reason. All truth is God's truth, and if you find truth through non-Christian means, then great. We must always be careful, however, to make the Bible the source of all revelation. Not some smart guy like Aristotle, but God's saving revelation through Jesus. It cannot always be explained. When reasoning and deduction fall short, we still must follow the Bible with faith like a child and know that all things will make sense some day.