NA61/SHINE is a fixed target experiment operating at the 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-μB) is being performed at the SPS by measurements of hadron production in proton-proton, proton-nucleus and nucleusnucleus interactions as a function of collision energy. In this paper the status of the NA61/SHINE strong interaction physics programme 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 in the produced matter and, therefore, have the ability to reveal the existence of the critical point via possible non-monotonic behavior. The NA61/SHINE results are compared to the model predictions.