The Hubble constant ($H_0$) tension is one of the biggest challenges in modern cosmology. This consists of the discrepancy, at around $5\sigma$, between the local value of $H_0$ measured through Supernovae Ia (SNe Ia) constrained with the Cepheids and the value inferred from the observations of Cosmic Microwave Background (CMB) by Planck data. According to the most appealing cosmological models, such as the flat $\Lambda$CDM, the $H_0$ should not vary according to the measurement method or the redshift $z$ of the probe used for estimating it. Thus, many ideas have been proposed in the literature to face this tension. In the current work, we summarize the results obtained with the binned analysis of SNe Ia, showing a decreasing trend for $H_0$ with $z$ with an evolutionary coefficient $\eta \sim 0.01$, and we further discuss the impact of high-$z$ probes such as Gamma-ray Bursts (GRBs) and quasars (QSOs) that allow reaching constraints on the cosmological parameters that will extend the Hubble diagram to high-$z$ values.