  A ($\kappa$,$\tau$)-regular set is a vertex subset S inducing a
$\kappa$-regular subgraph such that every vertex out of S has $\tau$ neighbors
in S. This article is an expository overview of the main results obtained for
graphs with ($\kappa$,$\tau$)-regular sets. The graphs with classical
combinatorial structures, like perfect matchings, Hamilton cycles, efficient
dominating sets, etc, are characterized by ($\kappa$,$\tau$)-regular sets whose
determination is equivalent to the determination of those classical
combinatorial structures. The characterization of graphs with these
combinatorial structures are presented. The determination of
($\kappa$,$\tau$)-regular sets in a finite number of steps is deduced and the
main spectral properties of these sets are described.
