This chapter concerns with the termination and/or bifurcation of the solution of delay differential equations with state-dependent delays. Two introductory examples illustrate where the termination/bifurcation phenomenon comes from and how a generalized solution may be defined after termination. Subsequently, a set of possible “regularization” of the problem, developed in the last few years for the numerical approximation of the generalized solution of state dependent delay differential equations with neutral term are presented and compared.
