The Brethren churches are, for the most part, German Baptist churches–descendants of the original Mennonite church formed when Menno, a German priest, became convinced of a radical interpretation of the Gospel.
The Amish, Mennonite, Brethren, and Dunkard churches all come from this movement. Generally the Brethren are the most liberal of the group; they don’t oppose any modern conveniences or inventions, and generally are most like liberal Baptists in their doctrine and practice. These churches practice only believers’ baptism, and although they celebrate a communion service, it’s seen as strictly memorial in nature.
Stricter Amish and Mennonite fellowships prohibit the use of a number of mechanical and electrical devices, and in general attempt to retain the simple manner of life practiced by the founders of this movement–with limited success lately, apparently, as younger members leave the church for the modern world.