We Shall present the results of a recent re-investigation of the spectral p
roperties of the Crab Nebula, based on the comparison between optical and X
-ray data. In this spectral range spatial variations of the synchrotron spe
ctrum show a detailed structure, for which we give a semi-empirical interpr
etation. The following components are spectrally singled out: the "torus",
with a flatter optical-to-X spectrum; a thick "equatorial" belt, in which f
eatures with little spectral bending roughly match the position of some the
rmal filaments; two "polar" lobes, whose spectra are highly bent and furthe
r soften going outwards. This kind of analysis is aimed to get a better und
erstanding of the acceleration processes inside this remnant, as well as ot
her plerions.