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