Despite the remarkable success of LCDM model to fit almost all of the cosmological observations, a non negligible difference of the amplitude of matter fluctuation $\sigma_8$ still persists between local and deep universe probes. We review the status of this potential discrepancy with outcomes from the latest probes, then we show, in particular, the results from our investigation on trying to reconcile the difference found between constraints on $\sigma_8$ using cluster counts and that obtained from CMB temperature and polarization angular power spectrum. For that we show the impact of three common extensions to LCDM model, i.e. massive neutrinos, a change in the growth index or that in the equation of state parameter of dark energy on the confidence contours of the value of $\sigma_8$ obtained from the aforementioned probes. We conclude at the end on the ability or not of these extensions to alleviate the tension.