  A critical discussion on the $H_0$ Hubble constant tension is presented by
considering both early and late-type observations. From recent precise
measurements, discrepancies emerge when comparing results for some cosmological
quantities obtained at different redshifts. We highlight the most relevant
measurements of $H_0$ and propose potential ideas to solve its tension. These
solutions concern the exploration of new physics beyond the $\Lambda$CDM model
or the evaluation of $H_0$ by other methods. In particular, we focus on the
role of the look-back time.
