The phase structure of QCD and the nature of the transition between ordinary hadronic matter and the deconfined state of quark-gluon plasma remain among the key open questions in high-energy physics. This talk will explore how these questions can be addressed using fluctuation observables, with a focus on event-by-event fluctuations in heavy-ion collisions and the search for the QCD critical point at finite baryon number density. I will discuss the dynamical description of proton number cumulants in heavy-ion collisions based on relativistic hydrodynamics, and the resulting constraints on the QCD critical point derived from recent data from the RHIC beam energy scan.