Using ~320h of good-quality Crab data from Feb 2007 to Apr 2014 the MAGIC telescopes measured the most energetic pulsed photons from a pulsar to date. The new results obtained probe the Crab Pulsar as the most compact TeV accelerator known to date. The remarkable detection of pulsed emission up to 1.5 TeV revealed by MAGIC imposes severe constraints on where and how the underlying electron population produces gamma-rays at these energies. Such TeV pulsed photons require a parent population of electrons with a Lorentz factor of at least 5E6. These results strongly suggest IC scattering off low-energy photons as the emission mechanism and a gamma-ray production region in the vicinity of the light cylinder, requiring a revision of the state-of-the-art models proposed to explain how and where gamma-ray pulsed emission from 100 MeV to 1.5 TeV are produced. Investigating the extension of the very high-energy spectral tail of the Crab Pulsar at energies above 400 GeV, the pulse profile was found to show two narrow peaks synchronized with those measured in the GeV energy range. The spectra of the two peaks follow two different power-law functions from 70 GeV up to 1.5 TeV and connect smoothly with the spectra measured above 10 GeV by the Large Area Telescope (LAT) on board the Fermi satellite.