  Extreme events gain the attention of researchers due to their utmost
importance in various contexts ranging from finance to climatology. This brings
such recurrent events to the limelight of attention in interdisciplinary
research. A comprehensive review of recent progress is provided to capture
recent improvements in analyzing such very high-amplitude events from the point
of view of dynamical systems and random walkers. We emphasize, in detail, the
mechanisms responsible for the emergence of such events in complex systems.
Several mechanisms that contribute to the occurrence of extreme events have
been elaborated that investigate the sources of instabilities leading to them.
In addition, we discuss the prediction of extreme events from two different
contexts, using dynamical instabilities and data-based machine learning
algorithms. Tracking of instabilities in the phase space is not always feasible
and precise knowledge of the dynamics of extreme events does not necessarily
help in forecasting extreme events. Moreover, in most studies on
high-dimensional systems, only a few degrees of freedom participate in extreme
events' formation. Thus, the notable inclusion of prediction through machine
learning is of enormous significance, particularly for those cases where the
governing equations of the model are explicitly unavailable. Besides, random
walks on complex networks can represent several transport processes, and
exceedances of the flux of walkers above a prescribed threshold may describe
extreme events. We unveil the theoretical studies on random walkers with their
enormous potential for applications in reducing extreme events. We cover the
possible controlling strategies, which may be helpful to mitigate extreme
events in physical situations like traffic jams, heavy load of web requests,
competition for shared resources, floods in the network of rivers, and many
more.
