  Photonic delay systems have revolutionized the hardware implementation of
Recurrent Neural Networks and Reservoir Computing in particular. The
fundamental principles of Reservoir Computing strongly benefit a realization in
such complex analog systems. Especially delay systems, potentially providing
large numbers of degrees of freedom even in simple architectures, can
efficiently be exploited for information processing. The numerous
demonstrations of their performance led to a revival of photonic Artificial
Neural Network. Today, an astonishing variety of physical substrates,
implementation techniques as well as network architectures based on this
approach have been successfully employed. Important fundamental aspects of
analog hardware Artificial Neural Networks have been investigated, and multiple
high-performance applications have been demonstrated. Here, we introduce and
explain the most relevant aspects of Artificial Neural Networks and delay
systems, the seminal experimental demonstrations of Reservoir Computing in
photonic delay systems, plus the most recent and advanced realizations.
