In this paper several problems arising when implementing methods to numerically solve delay-differential equations, such as overlapping, difficulties with error estimation, discontinuities of solution derivatives and the detection of such discontinuity points, are considered. Several approaches to each issue are discussed. The best solutions for explicit and diagonally implicit Runge-Kutta methods for DDEs are reported. A numerical comparison between a method implementing the handling of such problems, and the Matlab code ddesd, demonstrates that our method is more efficient.