Twenty years ago, we started to apply quantum optics to the astronomical research carried out inside the Department of Physics and Astronomy and the INAF Astronomical Observatory in Padova, Italy. The initial activities were stimulated by the project of the European Southern Observatory (ESO) to build a 100 m diameter telescope, the Overwhelmingly Large (OWL) telescope. The enormous photon flux expected from such an aperture suggested that quantum optics concepts be utilized in order to obtain novel astrophysical results. Following initial successful attempts to utilize the orbital angular momentum of the light beam to enhance the visibility of faint companions to bright stars, the Padova team concentrated its efforts on very high time resolution, in order to measure and store the arrival time of celestial photons to better than one nanosecond. To obtain observational results, we built two photon counting photometers (AquEye and IquEye) to be used with our telescopes of the Asiago Observatory and with 4 m class telescopes such as the ESO New Technology Telescope (NTT) in Chile. This paper firstly describes these two instruments and then expounds the results obtained on pulsar light curves, lunar occultations and the first photon counting intensity interferometry measurements of the bright star Vega. Indeed, the correlation of photon arrival times on two or more apertures can lead to extremely high angular resolutions, as shown around 1970 by Hanbury Brown and Twiss. Prospects for quantum intensity interferometry with arrays of Cherenkov light telescopes will also be described.