The NA61/SHINE experiment at the CERN SPS is a multipurpose fixed-target spectrometer for charged and neutral hadron measurements. Its research program includes studies of strong interactions as well as reference measurements for neutrino and cosmic-ray physics. One major goal of its strong interaction program is to determine the existence and pinpoint the location of the QCD critical point, an object of both experimental and theoretical studies. This contribution will summarize the current status of NA61/SHINE critical point searches in nucleus-nucleus collisions, in the collision energy range $\sqrt{s_{NN}} = 5-17$~GeV. The review includes studies of fluctuations of net-electric charge, femtoscopy analysis of $\pi-\pi$ pairs, as well as intermittency of protons and negatively charged hadrons. No clear indication of the critical point has been observed so far. Finally, we report on the development of novel methods aimed at solving the long-standing problem of bin-by-bin correlations in experimental intermittency analysis, and for a more accurate handling of systematics and uncertainties.

We present the first systematic measurement of the tilt of the pion emission source in relativistic Au+Au collisions at center-of-mass energies per nucleon pair, $\sqrt{s_{NN}}$ = 7.7, 14.5, 17.3 and 27 GeV, using data from the STAR experiment. The tilt angle and final freeze-out eccentricity are extracted through azimuthally sensitive femtoscopy of identical pion pairs. Our results reveal a strong dependence of the tilt parameter on the pair transverse momentum, indicating that the apparent source geometry is strongly coupled to expansion dynamics. Moreover, we observe a rapid decrease of the tilt magnitude with increasing collision energy, consistent with the emission source approaching longitudinal boost invariance at higher energies. These findings demonstrate that the commonly assumed boost-invariant geometry is insufficient and highlight the necessity of exploring the spatial structure of a tilted source, which is required in hydrodynamic models to reproduce features of the longitudinally expanding system, such as the slope of the directed flow. Comparisons with the UrQMD transport model show that it reproduces the overall energy dependence of the tilt magnitude qualitatively, but not quantitatively.