  We review different methods of generating potentials such that the
one-dimensional Schr\"{o}dinger equation (ODSE) can be transformed into the
hypergeometric equation. We compare our results with previous studies, and
complement the subject with new findings. Our main result is to derive new
classes of potentials such that the ODSE can be transformed into the Heun
equation and its confluent cases. The generalized Heun equation is also
considered.
