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Systems that exhibit complex behaviours are often found in a particulardynamical condition, poised between order and disorder. This observation is atthe core of the so-called criticality hypothesis, which states that systems ina dynamical regime between order and disorder attain the highest level ofcomputational capabilities and achieve an optimal trade-off between robustnessand flexibility. Recent results in cellular and evolutionary biology,neuroscience and computer science have revitalised the interest in thecriticality hypothesis, emphasising its role as a viable candidate general lawin adaptive complex systems. In this paper we provide an overview of the workson dynamical criticality that are -to the best of our knowledge- particularlyrelevant for the criticality hypothesis. We review the main contributionsconcerning dynamics and information processing at the edge of chaos, and weillustrate the main achievements in the study of critical dynamics inbiological systems. Finally, we discuss open questions and propose an agendafor future work.

Dynamical criticality: overview and open questions