So, I know that the puritans had some basic and profound beliefs, such as predestination and rejection of texts other than the bible. But, there aren't puritans walking around today, or at least I think not. So did their beliefs transform into any religious institutions that still exist? I am wondering specifically about the political and theological transformation over time. edited for grammar
there aren't puritans walking around today, or at least I think not
In the United States, the Presbyterians are probably the largest denomination descended from the Puritans.
There are also numerous congregations here of Reformed Calvinists, who are more closely related to the Dutch Reformed Church, which was (among other things) the de facto state religion of South Africa during the apartheid era.
The real story is a little more complicated - lots of groups labeled as "Puritan" were Nonconformists, so related to all kinds of littler Protestant denominations. And I shouldn't skip over the Congregationalists, who I don't know nearly enough about to speak authoritatively.
I do know that they would include the United Church of Christ and other "Mainline Protestant" groups, and have roots in the United States going back to the 1600s.
Both Oliver Cromwell and Jonathan Edwards are claimed as members by today's Congregationalists.
The Congregational Churches are the direct descendants of the Puritan churches in Massachusetts.
Because Congregational churches have maintained that there is no higher authority that each church reports to than its own congregation, there has been more diversity of doctrine and belief among Congregational churches than among some other more hierarchical churches.
Many Congregational churches adopted a "Unitarian" theology around 1800, and in 1825 the Unitarian Congregationalists separated from the rest of Congregationalism.
In 1957, Congregational Churches which were members of "The General Council of Congregational Christian churches in the United States" merged with the "Evangelical and Reformed Church" to form "The United Church of Christ".
So, today the Puritan churches have either remained "Congregational Churches" or 'morphed' into "United Church of Christ Churches", or 'morphed' into "Unitarian Churches" in the main. (There have also been some smaller and less important 'morphings'.)
For American History, I would examine the "First Great Awakening" in U.S. history as when many people broke away from Congregational teaching and started to follow the "New Light" ministers who represented Methodist and Baptist teachings. Also see the "2nd Great Awakening" as well. By the 1830s, tax-supported Congregationalist churches had faded away in the United States.