  The brain is a complex organ characterized by heterogeneous patterns of
structural connections supporting unparalleled feats of cognition and a wide
range of behaviors. New noninvasive imaging techniques now allow these patterns
to be carefully and comprehensively mapped in individual humans and animals.
Yet, it remains a fundamental challenge to understand how the brain's
structural wiring supports cognitive processes, with major implications for the
personalized treatment of mental health disorders. Here, we review recent
efforts to meet this challenge that draw on intuitions, models, and theories
from physics, spanning the domains of statistical mechanics, information
theory, and dynamical systems and control. We begin by considering the
organizing principles of brain network architecture instantiated in structural
wiring under constraints of symmetry, spatial embedding, and energy
minimization. We next consider models of brain network function that stipulate
how neural activity propagates along these structural connections, producing
the long-range interactions and collective dynamics that support a rich
repertoire of system functions. Finally, we consider perturbative experiments
and models for brain network control, which leverage the physics of signal
transmission along structural wires to infer intrinsic control processes that
support goal-directed behavior and to inform stimulation-based therapies for
neurological disease and psychiatric disorders. Throughout, we highlight
several open questions in the physics of brain network structure, function, and
control that will require creative efforts from physicists willing to brave the
complexities of living matter.
