  The problem of reconstructing nonlinear and complex dynamical systems from
measured data or time series is central to many scientific disciplines
including physical, biological, computer, and social sciences, as well as
engineering and economics. In this paper, we review the recent advances in this
forefront and rapidly evolving field, aiming to cover topics such as
compressive sensing (a novel optimization paradigm for sparse-signal
reconstruction), noised-induced dynamical mapping, perturbations, reverse
engineering, synchronization, inner composition alignment, global silencing,
Granger Causality and alternative optimization algorithms. Often, these rely on
various concepts from statistical and nonlinear physics such as phase
transitions, bifurcation, stabilities, and robustness. The methodologies have
the potential to significantly improve our ability to understand a variety of
complex dynamical systems ranging from gene regulatory systems to social
networks towards the ultimate goal of controlling such systems. Despite recent
progress, many challenges remain. A purpose of this Review is then to point out
the specific difficulties as they arise from different contexts, so as to
stimulate further efforts in this interdisciplinary field.
