The Crab Nebula and Its Mysteries: Some Facts and Puzzles

We discuss and summarize five results that we and various colleagues have produced over the last few years in the study of the wonderful, yet enigmatic, Crab Nebula and its pulsar. The results, in turn, have to do with the geometry inferred from Chandra X-ray observations, the surprising results of pulse phase polarimetry at 1.4 GHz, the search for an X-ray location of the gamma-ray flares for which we have Agile and Fermi to thank, and seeing if the optical and infrared inner knot might be the location of these flares.