  Systems that exhibit complex behaviours are often found in a particular
dynamical condition, poised between order and disorder. This observation is at
the core of the so-called criticality hypothesis, which states that systems in
a dynamical regime between order and disorder attain the highest level of
computational capabilities and achieve an optimal trade-off between robustness
and flexibility. Recent results in cellular and evolutionary biology,
neuroscience and computer science have revitalised the interest in the
criticality hypothesis, emphasising its role as a viable candidate general law
in adaptive complex systems. In this paper we provide an overview of the works
on dynamical criticality that are -to the best of our knowledge- particularly
relevant for the criticality hypothesis. We review the main contributions
concerning dynamics and information processing at the edge of chaos, and we
illustrate the main achievements in the study of critical dynamics in
biological systems. Finally, we discuss open questions and propose an agenda
for future work.
