We review in this paper the main results recently obtained on the identification and study of very high-z galaxies using lensing clusters as natural gravitational telescopes. We present in detail our pilot survey with ISAAC/VLT, aimed at the detection of z$>7$ sources. Evolutionary synthesis models for extremely metal-poor and PopIII starbursts have been used to derive the observational properties expected for these high-$z$ galaxies, such as expected magnitudes and colors, line fluxes for the main emission lines, etc. These models have allowed to define fairly robust selection criteria to find z$\sim 7-10$ galaxies based on broad-band near-IR photometry in combination with the traditional Lyman drop-out technique. The first results issued from our photometric and spectroscopic survey are discussed, in particular the preliminary confirmation rate, and the global properties of our high-z candidates, including the latest results on the possible z=10.0 candidate A1835-1916. The search efficiency should be significantly improved by the future near-IR multi-object ground-based and space facilities. However, strong lensing clusters remain a factor of $\sim$ 5-10 more efficient than blank fields in the z $\sim$ 7-11 domain, within the FOV of a few arcminutes around the cluster core, for the typical depth required for this survey project.