The detail
In Zurich a group of Zwingli's younger followers, including Conrad Grebel and Felix Manz, concluded that Scripture gave no basis for infant baptism and that the reform was moving too slowly because it depended on the city council. After a public disputation the council ordered infants to be baptised. On 21 January 1525, in Manz's house, Grebel baptised the former priest George Blaurock, who then baptised the others. Opponents called them Anabaptists ("re-baptisers"); they themselves held that infant baptism was not true baptism, so they were not baptising again.
Their theology centred on the church as a voluntary community of believers baptised on confession of faith, discipline within the congregation (the "ban"), a literal following of the Sermon on the Mount, refusal of oaths and, for most, of the sword, and separation of the church from civil government. The Schleitheim Confession (1527), drafted mainly by Michael Sattler, summarised these points in seven articles. The term "Radical Reformation", popularised by the historian George Huntston Williams (1962), also covers spiritualists and anti-Trinitarian groups that differed sharply from the Swiss Brethren.
Because they rejected the union of church and civil community, Anabaptists were seen as a threat to social order. Felix Manz was drowned in Zurich in January 1527 and Sattler was executed in Rottenburg that same year; the Diet of Speyer (1529) made rebaptism a capital offence across the Empire. Thousands were executed by Catholic and Protestant authorities. The violent seizure of Münster (1534–1535) by apocalyptic radicals, though rejected by most Anabaptists, was used for centuries to discredit the whole movement.
After Münster, the former Dutch priest Menno Simons (who left the priesthood in 1536) gathered scattered groups around a firmly peaceful practice; his followers became the Mennonites. In Moravia, Jakob Hutter organised communities with shared goods (the Hutterites), and in 1693 a split among Swiss and Alsatian Mennonites led by Jakob Ammann produced the Amish. Many emigrated in search of tolerance to the Netherlands, Prussia, Russia and later North and South America, including Paraguay and Argentina.
How each side tells it: for 16th-century Catholics and magisterial Protestants alike, Anabaptists were dangerous sectarians and heretics. Mennonite historians, especially after Harold Bender's "The Anabaptist Vision" (1944), present them as consistent heirs of the Reformation principle of Scripture and as pioneers of religious freedom and church–state separation; later scholars have stressed the movement's diversity. Reconciliation has followed: the Lutheran World Federation formally asked Mennonites for forgiveness for past persecution (Stuttgart, 2010), and Catholic–Mennonite dialogue produced the report "Called Together to Be Peacemakers" (1998–2003). Baptists, though historically distinct, share their emphasis on believer's baptism.