Flow and flow fluctuations in relativistic heavy-ion collisions

Relativistic heavy-ion collisions probe the extreme high-temperature regime of the strong interactions. Results from these experiments indicate the existence of a strongly-coupled Quark-Gluon Plasma with extremely small viscosity. One of the most important indications of
this is the strong collective behavior implied by "elliptic flow" measurements. Recently it was noticed that event-by-event fluctuations can have significant effects whose implications were not
previously appreciated. In particular, all long-range two-particle correlations can now be explained by collective flow alone. In addition, this new understanding suggests a number of additional independent "flow" observables that can be used to tightly constrain theoretical models, some of which have recently been measured. After an introduction and review of collective behavior in heavy-ion collisions I summarize some recent progress in understanding the effects of flow fluctuations and discuss what can be learned from these new measurements.