  Self-organized criticality has been proposed to be a universal mechanism for
the emergence of scale-free dynamics in many complex systems, and possibly in
the brain. While such scale-free patterns were identified experimentally in
many different types of neural recordings, the biological principles behind
their emergence remained unknown. Utilizing different network models and
motivated by experimental observations, synaptic plasticity was proposed as a
possible mechanism to self-organize brain dynamics towards a critical point. In
this review, we discuss how various biologically plausible plasticity rules
operating across multiple timescales are implemented in the models and how they
alter the network's dynamical state through modification of number and strength
of the connections between the neurons. Some of these rules help to stabilize
criticality, some need additional mechanisms to prevent divergence from the
critical state. We propose that rules that are capable of bringing the network
to criticality can be classified by how long the near-critical dynamics
persists after their disabling. Finally, we discuss the role of
self-organization and criticality in computation. Overall, the concept of
criticality helps to shed light on brain function and self-organization, yet
the overall dynamics of living neural networks seem to harnesses not only
criticality for computation, but also deviations thereof.
