  We review the basic properties of effective actions of families of theories
(i.e., the actions depending on additional non-perturbative moduli along with
perturbative couplings), and their description in terms of operators (called
check-operators), which act on the moduli space. It is this approach that led
to constructing the (quantum) spectral curves and what is now nicknamed the
EO/AMM topological recursion. We explain how the non-commutative algebra of
check-operators is related to the modular kernels and how symplectic (special)
geometry emerges from it in the classical (Seiberg-Witten) limit, where the
quantum integrable structures turn into the well studied classical
integrability. As time goes, these results turn applicable to more and more
theories of physical importance, supporting the old idea that many universality
classes of low-energy effective theories contain matrix model
