The surprising Crab pulsar and its nebula: A review

The Crab nebula and its pulsar (referred to together as "Crab") have historically played a central role in astrophysics. True to their legacy, several unique discoveries have been made recently. The Crab was found to emit gamma-ray pulsations up to energies of 400 GeV, beyond what was previously expected from pulsars. Strong gamma-ray flares, of durations of a few days were discovered from within the nebula, while the source was previously expected to be stable in flux on these time scales. Here we review these intriguing and suggestive developments. In this context we give an overview of the observational properties of the Crab and our current understanding of pulsars and their nebulae.