  Deciphering the underpinnings of the dynamical processes leading to
information transmission, processing, and storing in the brain is a crucial
challenge in neuroscience. An inspiring but speculative theoretical idea is
that such dynamics should operate at the brink of a phase transition, i.e., at
the edge between different collective phases, to entail a rich dynamical
repertoire and optimize functional capabilities. In recent years, research
guided by the advent of high-throughput data and new theoretical developments
has contributed to making a quantitative validation of such a hypothesis. Here
we review recent advances in this field, stressing our contributions. In
particular, we use data from thousands of individually recorded neurons in the
mouse brain and tools such as a phenomenological renormalization group
analysis, theory of disordered systems, and random matrix theory. These
combined approaches provide novel evidence of quasi-universal scaling and
near-critical behavior emerging in different brain regions. Moreover, we design
artificial neural networks under the reservoir-computing paradigm and show that
their internal dynamical states become near critical when we tune the networks
for optimal performance. These results not only open new perspectives for
understanding the ultimate principles guiding brain function but also towards
the development of brain-inspired, neuromorphic computation.
