Fluctuation observables are invaluable tools in relativistic heavy ion collisions to investigate primordial thermodynamics of fireballs. Active experimental measurements have been performed at RHIC and LHC. In particular, interesting experimental results were recently reported on the electric charge fluctuation at ALICE and on the higher order cumulants at STAR, which show nontrivial behaviors reflecting non-hadronic and/or non-thermal physics. We argue that more detailed understanding on these observables are needed to use them effectively in the analysis of QCD phase structure. We suggest that the measurement of various cumulants of conserved charges including baryon number and their rapidity window dependence will provide important information needed for making progress in this subject. (C) 2014 Elsevier B.V. All rights reserved.