  In this article we outline the historical development and key results
obtained to date for free parafermionic spin chains. The concept of free
parafermions provides a natural N-state generalization of free fermions, which
have long underpinned the exact solution and application of widely studied
quantum spin chains and their classical counterparts. In particular, we discuss
the Baxter-Fendley free parafermionic Z(N) spin chain, which is a relatively
simple non-Hermitian generalization of the Ising model.
