Let \(G\) be a group having a finite composition series. Then the set \(R(G)\) of all subnormal subgroups of \(G\) is a sublattice of the lattice \(L(G)\) of all subgroups of \(G\). If \(\tau\) is an equivalence relation on the set \(R(G)\), the \textit{lower kernel} \(N_\tau\) of \(\tau\) is the subgroup generated by all elements of \(R(G)\) which are \(\tau\)-equivalent to the identity subgroup \(\{1\}\) of \(G\), and the \textit{upper kernel} \(N^\tau\) of \(\tau\) is the intersection of all elements of \(R(G)\) which are \(\tau\)-equivalent to \(G\) itself. In this survey article the author studies the behaviour of the subgroups \(N_\tau\) and \(N^\tau\), for a congruence \(\tau\) of the lattice \(R(G)\), where \(G\) is a group with a finite composition series. The last part of the article is devoted to the characterization of finite soluble groups \(G\) for which the lattice \(R(G)\) admits a congruence \(\tau\) such that \(R(G)/\tau\) is a non-trivial chain.