  We give a precise definition of folded quivers and folded cluster algebras.
We give many examples of including some with finite mutation structure that do
not have analogues in the unfolded cases. We relate these examples to the
finite mutation type quivers $X_6$ and $X_7$. We also construct a folded
cluster algebra associated to triangulations of punctured surface which allow
for triangulations self-folded triangles. We give a simple construction of a
folded cluster algebra for which the cluster complex is a generalized
permutohedron.
