  Real-world non-autonomous systems are open, out-of-equilibrium systems that
evolve in and are driven by temporally varying environments. Such systems can
show multiple timescale and transient dynamics together with transitions to
very different and, at times, even disastrous dynamical regimes. Since such
critical transitions disrupt the systems' intended or desired functionality, it
is crucial to understand the underlying mechanisms, to identify precursors of
such transitions and to reliably detect them in time series of suitable system
observables to enable forecasts. This review critically assesses the various
steps of investigation involved in time-series-analysis-based detection of
critical transitions in real-world non-autonomous systems: from the data
recording to evaluating the reliability of offline and online detections. It
will highlight pros and cons to stimulate further developments, which would be
necessary to advance understanding and forecasting nonlinear behavior such as
critical transitions in complex systems.
