  The time needed to exchange information in the physical world induces a delay
term when the respective system is modeled by differential equations. Time
delays are hence ubiquitous, being furthermore likely to induce instabilities
and with it various kinds of chaotic phases. Which are then the possible types
of time delays, induced chaotic states, and methods suitable to characterize
the resulting dynamics? This review presents an overview of the field that
includes an in-depth discussion of the most important results, of the standard
numerical approaches and of several novel tests for identifying chaos. Special
emphasis is placed on a structured representation that is straightforward to
follow. Several educational examples are included in addition as entry points
to the rapidly developing field of time delay systems.
