  The ability to harness the dynamics of quantum information and entanglement
is necessary for the development of quantum technologies and the study of
complex quantum systems. On the theoretical side the dynamics of quantum
information is a topic that is helping us unify and confront common problems in
otherwise disparate fields in physics, such as quantum statistical mechanics
and cosmology. On the experimental side the impressive developments on the
manipulation of neutral atoms and trapped ions are providing new capabilities
to probe their quantum dynamics. Here, we overview and discuss progress in
characterizing and understanding the dynamics of quantum entanglement and
information scrambling in quantum many-body systems. The level of control
attainable over both the internal and external degrees of freedom of individual
particles in these systems provides great insight into the intrinsic connection
between entanglement and thermodynamics, bounds on information transport and
computational complexity of interacting systems. In turn this understanding
should enable the realization of quantum technologies.
