  This chapter presents a dynamical systems point of view of the study of
systems with delays. The focus is on how advanced tools from bifurcation
theory, as implemented for example in the package DDE-BIFTOOL, can be applied
to the study of delay differential equations (DDEs) arising in applications,
including those that feature state-dependent delays. We discuss the present
capabilities of the most recent release of DDE-BIFTOOL. They include the
numerical continuation of steady states, periodic orbits and their bifurcations
of codimension one, as well as the detection of certain bifurcations of
codimension two and the calculation of their normal forms. Two longer case
studies, of a conceptual DDE model for the El Nino phenomenon and of a
prototypical scalar DDE with two state-dependent feedback terms, demonstrate
what kind of insights can be obtained in this way.
