The Reformation itself has a fairly well-known set of players and movements. The common divisions are:
We sometimes think of the Lutheran Reformation as the work of only one person. We could be forgiven for thinking this; it was, after all, Luther's 95 Theses pinned on the door of the Wittenberg church in 1517 that set things off. But it was not so simple – Luther was set up for this by the work of various reformers before, some of whom had lost their lives at an earlier time when the pope was stronger in various parts of Europe than he was by the early 16th century.
The Lutheran reformation was predominantly an academic event, at least at the beginning. The complaint was that the Catholic church had flawed theology. Specifically, the doctrine of justification required rethinking. It was only after 1522, after Luther returned to Wittenberg, that the movement took on the trappings of a society-wide reform, rather than just an academic dispute. The actual social reforms of the movement were actually quite limited, and not all that successful. Lutheran thought remained tied to German territories, and later Scandinavia, but little beyond that.
It was not long after Luther that the Lutheran reformation started to take on two distinct sides. One side was that of the new theology that Luther had instituted. His argument, after all, was that the Catholics had bad theology. Many of his followers interpreted his Reformation as an attempt to correct that theology. If you tie that to his relationships with various princes, you have a ready-made church hierarchy. By the early 17th century, people already know that the Lutheran orthodoxy was every bit as strong as any earlier Catholic structure.
The other side was that which took seriously the idea that Luther wanted a religion of the heart. It was not just that it was new theology; it was theology that freed people by allowing them to follow the best evidence of their heart. This is part of the birth of Pietism, and had much more of a moral aspect to it. It is the side of Lutheranism that takes seriously the heritage from earlier reformers and texts, such as Johann Tauler and the Theologica Germanica.
The Lutheran Reformation met with a kind of peace by 1555 in the Peace of Augsburg, which divided Germany up into provinces that were either Catholic or Lutheran. You were what your region was.
While the Lutheran movement was mostly a German affair, the Reformed movement was Swiss, and later Dutch. The power base started in Zurich, went to Berne, and finally ended up in Geneva, Calvin's home. But, it extended from there to be the more wide-spread movement. It had perhaps the most significant effect on Britain, and eventually North America. The Presbyterians and the Methodists in Scotland and England basically have Reformed theology, and the Puritans have a kind of combination of Pietism (which spans all the traditions) and Reformed thought.
While the Lutheran reformation was primarily an academic affair, directed at bad theology, the Reformed movement tended to be a populist affair, directed at bad practice. Doctrine became significant, especially by the time of Calvin, but early on there was little interest in it. They wanted to reform institutions, governments, and cities. All the major early Reformed theologians had strongly humanistic leanings, while Luther was always at least in part at odds with the humanistic side of his movement (Philip Melanchthon, and Erasmus to a certain extent, although he was never a Lutheran).
Although the Reformed movement was not part of the Peace of Augsburg (which meant that it had no place in Germany), with the Heidelburg Catechism 1563 it had gained a foothold in many places in Europe.
No one much liked the radical reformers. They were seen as theologically radical even by the other movements of the Reformation. Even today if you read theologians in either of the two "magisterial Reformation" traditions, there is a general disdain for Anabaptist theology. What is this theology? It involves several aspects: 1. The peace position is central; 2. Separation from the world and secular structures of power is important; 3. There is a move away from structure and image in worship; 4. As the name "Anabaptist" suggests, there is the requirement for rebaptism, if a person was baptized as a child. This is because of the conviction that only a person with the free will to choose, can decide his or her spiritual state. Therefore, only adults can choose.
As mentioned, no one seemed to like the Radical Reformers much. There is a book that is legendary in Anabaptist circles called the Martyr's Mirror. It recounts the deaths of Anabaptists at the hands of everyone, including the other Reformation traditions. The rhetoric, as well as the action, was extreme during this time.
The Anabaptists basically went to whatever country would take them. Many stayed in Holland and Belgium, until Catherine the Great in Russia needed farmers to show the locals how to do it, and also establish control over certain parts of Russia and the Ukraine. Lots of Mennonites went there. Some Anabaptists came to North America early on, and formed Amish, Hutterite, and Mennonite communities.
What are the Catholics doing during this time? The Catholic Church recognized the need for reform, as well as the need to counter the claims of the major reformers. In 1545 the Council of Trent opened, and particularly in Spain and Italy there were reforms in the clergy, in religious education, and in missionary activity. This was the time that the Jesuits were established, for example, with the mission to evangelize and educate. They become a major factor in the soon-to-come explorations of the new world. So, there were changes within the church itself during this time that attempted to deal with some of the excesses of the time. Alas, it was too little too late to stem the Protestant tide, but at least it was not simply a destructive or vindictive reaction (although there was some of that as well).
Some countries remain very much within the Catholic fold. Spain, France, and Italy all are solidly Catholic, but it changes over time in all these places. In Spain, there was a very devout king, King Philip, who kept the church very high in the minds of all the people. If you look at the spirituality that develops there, though, you find shifts. It was the time of Theresa of Avila and St. John of the Cross. These were Discalced Carmelites, a new kind of order that emphasized personal spirituality over the more Platonic spirituality of earlier days. When John writes the Dark Night of the Soul, for example, he gives us a kind of psychology of spirituality. He tries to account for all the barriers that different people may have to "climb Mt. Carmel". These barriers are variations on the weakness of the flesh, but the point is that there is an acknowledgment of individuality here.