Amish History
The Amish history starts in Switzerland back at the end of the 1600s, when Jakob Ammann disagreed with the Swiss Mennonites about two simple things: how to dress and how to worship.
Jakob Ammann, together with a group of people that agreed with him, separated from the Swiss Mennonites and they have since been called the Amish or the Amish Mennonites. (Amish comes from Ammann.)
This group of Amish people grew over the years in Europe, but poverty and religious disagreements caused them look for new places to live. A large migration started in the beginning of the 1700s and continued for more than 100 years. They first ended up in Pennsylvania, then eventually spread to other states. Amish people can now be found in about half of all US States, in addition to Canada, and even in Central America. Although, note that the greatest populations of Amish can still be found in Pennsylvania, Ohio, and Indiana.
PS. The Swiss Mennonites "back home" still exist, and are obviously very similar to the Amish people.