The dynamical systems viewpoint of autonomous differential equations with finite or bounded delays has developed to investigate the long-term or asymptotic behavior of solutions of such equations. However, as Walther (2003) pointed out, if the delays depend on an unknown function (called the state-dependent delays), the above theory cannot be applied. Furthermore, if we permit the dependence of the delays on time and state, then the possibility of unbounded delays arise, and the dynamics become nonautonomous.

In this talk, we first review the above contents. Next, we obtain a semi-dynamical system for differential equations with unbounded delays. Finally, we find and apply the theory of global attractor and the pullback attractor for such equations.