The groundwork for Zwingli's and Calvin's theologies, which led to the creation of Reformed and Presbyterian churches, was laid by three intellectual and cultural movements: Renaissance humanism, late medieval nominalism, and mysticism.
The Renaissance is a cultural and intellectual movement in the 14th to the 16th centuries in Europe that placed a high value on the classical art and philosophy of ancient Greece and Rome. "Renaissance" literally means "rebirth," and Renaissance thinkers saw themselves as the rebirth of classical culture (they coined the term "Middle Ages" or "Dark Ages" to denote the centuries standing between classical culture and their own). Michelangelo and Leonardo da Vinci are Italian Renaissance artists who often depicted scenes from classical sources, and tried to build off Greek ideas of symmetry and beauty.
Humanism is a movement within the Renaissance that turned from what they saw as nit-picky medieval speculation (they have people like Thomas Aquinas) in mind and focused on classical texts in their original languages as a means to educate moral people dedicated to civic virtue. The motto of humanism (in Latin) is "ad fontes"-"to the sources." Zwingli and Calvin both trained as humanists. Zwingli studied in the center of humanist studies, the University of Basel, and revered Erasmus, the greatest of the humanists. Erasmus himself wavered on the Reformation, but finally chose to remain within the Roman Catholic Church.
When Erasmus published the New Testament in the original Greek, based on the best original manuscripts available (the official Catholic Bible was a Latin translation), Zwingli (then a young parish priest) bought a copy, and then taught himself Greek so he could read it. It was humanism that led Zwingli later to announce that he would preach the Gospels straight through, rather than from a lectionary. John Calvin also trained as a humanist-in fact his first book was on Cicero, the great Roman politician, philosopher, and orator. Renaissance humanism influenced both founders to trust the Bible as a source of renewal for the Church, and to place it above the Church as an authority.
Nominalism was a strand of medieval philosophy in the tradition of (but also critical of) the philosophy of Thomas Aquinas. Thomas, relying on Aristotle, argued that everything is what it is because it has a divine essence, and that humans know things because our minds share these essences. The most famous nominalist was William Ockham. His principle, known as "Ockham's razor," was that, all things being equal, the simplest explanation was the best explanation. Ockham argued that humans know things because we lump individual things together into categories, and give categories names (hence, "nominalism"). He requires only two kinds of things in the world to explain how we know the world: things and minds. His razor has cut away Thomas's divine essences.
All the major reformers-Martin Luther, Huldrych Zwingli, and John Calvin-were influenced by nominalism. The consequence of this influence is that they did not think that one could know anything about God by looking at the world. Although God created the world, our minds did not have access to divine essences in the world that would teach us about God. We could not draw analogies from the world to God. Our only knowledge of God came from what God chose to reveal in scripture. Scripture does not answer speculative questions about the nature of God, or why God set up the world as it is. It only tells us that we are sinners, but that God promises forgiveness.
In the late Middle Ages mysticism, the attempt to discipline one's life in such a way that immediate contact with the divine is possible, became more popular. Christianity has a long tradition of mysticism. Gerhard Groote (1340-1384) founded the Brethren of the Common life, a community of mystics for lay men and women. This community is one example of dissatisfaction with available forms of piety in the late Middle Ages, and experimentation with new religious forms. The example of this attempt to focus on the personal experiential life of laity rather than on correct doctrine was an important model for the Reformers.
Finally, many social factors created a receptive environment for the Reformed founders and the Protestant movement. The 16th century was a time of rapid urbanization (and the early Reformation was largely a city affair). Reformers benefitted from the invention of the moveable type printing press. During this time there was a middle class growing in size and prestige between the nobility and the peasants, and the first stirrings of nationalism (some branches of Protestantism quickly take on a national character). All these changes created anxiety and opportunity for new religious movements.