  We introduce super quantum Airy structures, which provide a supersymmetric
generalization of quantum Airy structures. We prove that to a given super
quantum Airy structure one can assign a unique set of free energies, which
satisfy a supersymmetric generalization of the topological recursion. We reveal
and discuss various properties of these supersymmetric structures, in
particular their gauge transformations, classical limit, peculiar role of
fermionic variables, and graphical representation of recursion relations.
Furthermore, we present various examples of super quantum Airy structures, both
finite-dimensional -- which include well known superalgebras and super
Frobenius algebras, and whose classification scheme we also discuss -- as well
as infinite-dimensional, that arise in the realm of vertex operator super
algebras.
