  In modern mathematical and theoretical physics various generalizations, in
particular supersymmetric or quantum, of Riemann surfaces and complex algebraic
curves play a prominent role. We show that such supersymmetric and quantum
generalizations can be combined together, and construct supersymmetric quantum
curves, or super-quantum curves for short. Our analysis is conducted in the
formalism of super-eigenvalue models: we introduce $\beta$-deformed version of
those models, and derive differential equations for associated
$\alpha/\beta$-deformed super-matrix integrals. We show that for a given model
there exists an infinite number of such differential equations, which we
identify as super-quantum curves, and which are in one-to-one correspondence
with, and have the structure of, super-Virasoro singular vectors. We discuss
potential applications of super-quantum curves and prospects of other
generalizations.
