Initial state fluctuations and final state correlations in relativistic heavy-ion collisions

We review the phenomenology and theory of bulk observables in ultrarelativistic heavy-ion collisions, focusing on recent developments involving event-by-event fluctuations in the initial stages of a heavy-ion collision, and how they manifest in observed correlations. We first define the relevant observables and show how each measurement is related to underlying theoretical quantities. Then we review the prevailing picture of the various stages of a collision, including the state-of-the-art modeling of the initial stages of a collision and subsequent hydrodynamic evolution, as well as hadronic scattering and freeze-out in the later stages. We then discuss the recent results that have shaped our current understanding and identify the challenges that remain. Finally, we point out open issues and the potential for progress in the field.