We searched for gamma-ray sources at energies above 10 GeV using data from the Large Area Telescope (LAT) accumulated during the first 3 years of the Fermi Gamma-ray Space Telescope mission. We detected 516 sources with a Test Statistic (TS) larger than 25, measured their spectra, quantified their variability, and studied their associations with cataloged sources at other wavelengths. We found that 453 (88%) objects could be associated with known sources, out of which 393 (76%) are AGNs. This list complements the Second Fermi LAT catalog, which was based on 2 years of data extending down to 100 MeV and so included many sources with softer spectra. In the conference we will also report on the population implications and highlight the subset of sources that are good candidates for detection at energies above 50-100 GeV with currently operating and future Cherenkov telescope facilities.