We study the redshift evolution of the quasar (QSO) UV luminosity function (LF) for 0.5 < z < 6.5, by collecting the most up to date observational data and, in particular, the recently discovered population of faint active galactic nuclei (AGNs). We fit the QSO LF using either a double power-law function or a Schechter function, finding that both forms provide good fits to the data. We derive empirical relations for the LF parameters as a function of redshift and, based on these results, predict the QSO UV LF at z = 8. From the inferred LF evolution, we compute the redshift evolution of the QSO/AGN comoving ionizing emissivity and hydrogen photoionization rate. If faint AGNs are included, the contribution of QSOs to reionization increases substantially. However, their level of contribution critically depends on the detailed shape of the QSO LF, which can be constrained by efficient searches of high-z QSOs. To this aim, we predict the expected (i) number of z > 6 QSOs detectable by ongoing and future near-infrared surveys (as EUCLID and Wide-Field Infrared Survey Telescope), and (ii) number counts for a single radio-recombination line observation with Square Kilometre Array-MID (FoV = 0.49 deg2) as a function of the Hna flux density, at 0 < z < 8. These surveys (even at z < 6) will be fundamental to better constrain the role of QSOs as reionization sources.