## ABSTRACT

Heir-equations were found by iterating the nonclassical symmetry method. Apart from inheriting the same Lie symmetry algebra of the original partial differential equation, and thus yielding more (and different) symmetry solutions than expected, the heir-equations are connected to conditional Lie-Bäcklund symmetries, and generalized conditional symmetries; moreover they solve the inverse problem, namely a special solution corresponds to the nonclassical symmetry. A 25-year review of work is presented, and open problems are brought forward.