NA61/SHINE is a fixed target experiment operating at CERN SPS. Its main goals are to search for the critical point of strongly interacting matter and to study the onset of deconfinement. For these goals a scan of the two dimensional phase diagram (T−μ_B) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleus and nucleus-nucleus interactions as a function of collision energy. In this paper the status of the search for the critical point of strongly interacting matter by the NA61/SHINE Collaboration is presented including recent results on proton intermittency, strongly intensive fluctuation observables of multiplicity and transverse momentum fluctuations. These measurements are expected to be sensitive to the correlation length and, therefore, have the ability to reveal the existence of the critical point via possible non-monotonic behavior. The new NA61/SHINE results are compared to the model predictions.