  In this paper, we review our non-Bloch band theory in one-dimensional
non-Hermitian tight-binding systems. In our theory, it is shown that in
non-Hermitian systems, the Brillouin zone is determined so as to reproduce
continuum energy bands in a large open chain. By using simple models, we
explain the concept of the non-Bloch band theory and the method to calculate
the Brillouin zone. In particular, for the non-Hermitian Su-Schrieffer-Heeger
model, the bulk-edge correspondence can be established between the topological
invariant defined from our theory and existence of the topological edge states.
