Onset of deconfinement and search for the critical point of strongly interacting matter at CERN SPS energies

The exploration of the QCD phase diagram particularly the search for a phase transition from hadronic to partonic degrees of freedom and possibly a critical endpoint, is one of the most challenging tasks in present heavy-ion physics. As observed by the NA49 experiment, several hadronic observables in central Pb+Pb collisions at the CERN SPS show qualitative changes in their energy dependence. These features are not observed in elementary interactions and indi- cate the onset of a phase transition in the SPS energy range. The existence of a critical point is expected to result in the increase of event-by-event fluctuations of various hadronic observables provided that the freeze-out of the measured hadrons occurs close to its location in the phase di- agram and the evolution of the final hadron phase does not erase the fluctuations signals. Further information about the existence and nature of a phase transition in the SPS energy range can be gained from the studies of event-by-event fluctuations of final state hadron distributions and yields performed by NA61/SHINE, the successor of the NA49 experiment. Experimental results from both experiments on event-by-event fluctuations of transverse-momentum, multiplicity as well as low mass pion pair and proton number fluctuations are shown as a function of beam energy and system size.