Experimental progress in atomic, molecular, and optical platforms in the last decadehas stimulated strong and broad interest in the quantum coherent dynamics of manylong-range interactingparticles. The prominent collective character of these systems en-ables novel non-equilibrium phenomena with no counterpart in conventional quantumsystems with local interactions. Much of the theory work in this area either focussedon the impact of variable-range interaction tails on the physics of local interactions orrelied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recentadvances in the field. Working with prototypical interacting quantum spin latticeswithout disorder, our presentation hinges upon a versatile theoretical formalism thatinterpolates between the few-body mean-field physics and the many-body physics ofquasi-local interactions. Such a formalism allows us to connect these two regimes,providing both a formal quantitative tool and basic physical intuition. We leveragethis unifying framework to review several findings of the last decade, including thepeculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdownof entanglement dynamics, suppression of thermalization and equilibration, anomalousscaling of defects upon traversing criticality, dynamical phase transitions, and genuinelynon-equilibrium phases stabilized by periodic driving. The style of this Report is on thepedagogical side, which makes it accessible to readers without previous experience inthe subject matter. (c) 2024TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).
