The remarkable Crab Nebula is powered by an energetic pulsar whose relativistic wind interacts with the inner parts of the Supernova Remnant SN1054. Despite low-intensity optical and X-ray variations in the inner Nebula, the Crab has been considered until now substantially stable at X-ray and gamma-ray energies. This paradigm has been shattered by the AGILE discovery in September 2010 of a very intense transient gamma-ray flare of nebular origin. For the first time, the Crab Nebula was caught in the act of accelerating particles up to 10^15 eV within the shortest timescale ever observed in a cosmic nebula (1 day or less). Emission between 50 MeV and a few GeV was detected with a quite hard spectrum within a short timescale. Additional analysis and recent Crab Nebula data lead to identify a total of four major flaring gamma-ray episodes detected by AGILE and Fermi during the period mid-2007/mid-2011. These observations challenge emission models of the pulsar wind interaction and particle acceleration processes. Indeed, the discovery of fast and efficient gamma-ray transient emission from the Crab leads to substantially revise current models of particle acceleration.