Event-by-Event Observables and Fluctuations

In this talk the status and open questions of the phenomenological description of all the stages of a heavy ion reaction are highlighted. Special emphasis is put on event-by-event fluctuations and associated observables. The first part is concentrated on high RHIC and LHC energies and the second part reviews the challenges for modeling heavy ion reactions at lower beam energies in a more realistic fashion. Overall, the main conclusion is that sophisticated theoretical dynamical approaches that describe many observables in the same framework are essential for the quantitative understanding of the properties of hot and dense nuclear matter.