  We review the phenomenology and theory of bulk observables in
ultra-relativistic heavy-ion collisions, focussing 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.
