Some ramifications of the Lyapunov-Krasovskii Theory are explored. First, for linear delay systems the resulting sufficient conditions for robust asymptotic stability are related to the Schur-Cohn and the Hurwitz stability of the system matrices. Second, ideas towards a constructive parameterization for linear time-invariant delay systems are presented. Third, new applications for pseudo-linear systems are explored. Finally, some recent advances in the stability and stabilization for nonlinear systems are surveyed, which may be exploited in the arena of delay systems.