  Quantum circuits -- built from local unitary gates and local measurements --
are a new playground for quantum many-body physics and a tractable setting to
explore universal collective phenomena far-from-equilibrium. These models have
shed light on longstanding questions about thermalization and chaos, and on the
underlying universal dynamics of quantum information and entanglement. In
addition, such models generate new sets of questions and give rise to phenomena
with no traditional analog, such as new dynamical phases in quantum systems
that are monitored by an external observer. Quantum circuit dynamics is also
topical in view of experimental progress in building digital quantum simulators
that allow control of precisely these ingredients. Randomness in the circuit
elements allows a high level of theoretical control, with a key theme being
mappings between real-time quantum dynamics and effective classical lattice
models or dynamical processes. Many of the universal phenomena that can be
identified in this tractable setting apply to much wider classes of more
structured many-body dynamics.
