Another revision of Calvinism is called Amyrauldianism, "hypothetical universalism", or "four-point Calvinism", which asserts that Christ's death atones for the sins of all men, but only those who repent and believe are elect and receive forgiveness. This doctrine was most thoroughly systematized by the French Reformed theologian at the University of Saumur, Moses Amyraut, for whom it is named. It was popularized in England by the Reformed pastor Richard Baxter, and gained strong adherence in the Presbyterian church in American colonies, during the 17th and 18th centuries. In the United States, Amyrauldianism is the most common form of Calvinism current among evangelical churches. Baxter himself differentiated his proposals from those of Amyrauldianism, on several rather subtle points. Baxter's influential form of hypothetical universalism is often called neonomianism, and is generally considered a milder proposal of reform than Amyraut's version.

In the mainline Reformed churches, Calvinism has undergone significant revision through the influence of Karl Barth and neo-orthodox theology. Barth was an important Swiss Reformed theologian who began writing early in the 20th century, whose chief accomplishment was to counter-act the influence of the Enlightenment in the churches, especially as this had led to the toleration of Nazism in the Germanic countries of Western Europe. The Barmen declaration is an expression of the Barthian reform of Calvinism. The revisions Barth proposed are radical and impossible to concisely discuss in comparison to classical Calvinism but generally involve the complete rejection of natural theology. Conservative Calvinists (as well as some liberal reformers) regard it as confusing to use the name "Calvinism" to refer to neo-orthodoxy or the other liberal revisions mentioned above.

Conservative reforms
A more conservative revision of Calvinism gained influence in the Dutch Reformed churches, late in the 19th century, which has been dubbed "neo-Calvinism", and developed along lines of the theories of Dutch theologian, statesman and journalist, Abraham Kuyper. This revision was a response to the influences of the Enlightenment, but generally speaking did not touch directly on the articles of salvation. Neo-Calvinism is a revision of the Calvinist world-and-life view, which is an extension of the Calvinist understanding of salvation to scientific, social and political issues. In the United States, Kuyperian neo-Calvinism is represented among others, by the Center for Public Justice, a faith-based political think-tank headquartered in Washington, D.C.

Neo-Calvinism branched off in more conservative movements in the United States. The first of these to rise to prominence became apparent through the writings of Francis Schaeffer, and a group of scholars associated with a Calvinist study center in Switzerland, called L'abri. This movement generated a reawakened social consciousness among Evangelicals, especially in response to abortion, and was one of the formative influences which brought about the "Moral Majority" phenomenon in the United States, in the early 1980s.

A more radical Calvinist movement that has been influential in American family and political life is called Christian Reconstructionism. Reconstructionism is a separate revision of Kuyper's approach under the leadership of the late Rousas J Rushdoony, son of Armenian immigrants, Reformed scholar and essayist. The movement has marginal influence in some of the conservative Reformed churches in which it was born, and in Calvinistic Baptist and charismatic churches mostly in the United States. Not a political movement, strictly speaking, Reconstructionism has been influential in the development of the so-called "religious right"; it aims toward the complete reconstruction of the structures of society on Christian and Biblical presuppositions, although not in terms of "top down" structural changes, but through the steady advance of the Gospel of Christ as men and women are converted, and thus seek laws and structures that serve them best.

Hyper-Calvinism
Calvinism has frequently appeared in various forms, which are called hyper-Calvinism by critics of that version of doctrine, on the supposition that it is a corrupted form of Calvinism. Hyper-calvinism is not necessarily believed by anyone (indeed, it can't be believed in all of its varieties); it is a label applied to any extrapolation of a point of calvinism which undermines the theological system, sometimes mistakenly attributed to Calvinism by critics. The name "hyper-Calvinism" is also applied to beyond-orthodox reform movements, which attempt to improve Calvinism by removing perceived inconsistencies. Many Calvinists may reject as deplorable and hyper-Calvinistic, and destructive to the Christian faith, such beliefs as:

• that God is the source of sin and of evil
• that God from all eternity has acted to irresistibly compel men toward sin and unbelief, just as he pursues those upon whom he desires to have mercy
• that men have no will of their own, and secondary causes are of no effect
• that the number of the elect at any time may be known by men
• that it is wrong to evangelize
• that assurance of election must be sought prior to repentance and faith
• that men who have once sincerely professed belief are saved regardless of what they later do
• that God has chosen some races of men and has rejected others
• that the children of unbelievers dying in infancy are certainly damned
• that God does not command everyone to repent
• that the sacraments are not means of grace, but obstacles to salvation by faith alone.
• that the true church is only invisible, and salvation is not connected with the visible church
• that the Scriptures are intended to be interpreted by individuals only and not by the church.
• that no government is to be obeyed which does not acknowledge that Jesus is the Lord, or that Biblical Law is its source of authority
• that the grace of God does not work for the betterment of all men
• that saving faith is equivalent to belief in the doctrine of predestination
• that only Calvinists are Christians
  
  Of course, there are Calvinists who believe that these are not caricatures of Calvinism and conscientiously hold to some of them in the belief that these are a logical outworking of their faith. Such Calvinists vigorously object to being called "hyper-Calvinist".

The substance of Calvinism is total dependence on God. Every good thing any person has is there because of God's unmerited grace, and salvation is particularly dependent on grace. Calvinism is intentionally such that all credit, for everything, must go directly to God; humans are but miserable sinners. The "solas" exist to keep all the credit where it belongs, and to exclude any illicit additions such as those the Reformers claimed Catholics had made. The five solas were the summary of Calvinism, indeed of the Reformation, before the Framing of TULIP.