We present a detailed analysis of the morphological properties of the Crab Nebula across the electromagnetic spectrum based on new and previous high-quality data from radio to X-rays. In the radio range we obtained an image of the entire nebula at 3 GHz with subarcsecond angular resolution using the VLA (NRAO) and an image at 100 GHz of the central region using the ALMA array. Simultaneously with the VLA observations we performed HST WFPC3 near-infrared (lambda similar to 1.5 mu m) and Chandra X-ray (0.5-8 keV band) observations of the central region of the nebula. In addition we produced a new UV image of the Crab Nebula at 291 nm by co-adding 75 individual exposures of the Optical-UV Monitor on board XMM-Newton. The high-angular resolution and high-dynamic range radio image at 3 GHz allowed us to improve the detection and characterization of peculiar morphological features including arches with foot brightening and intercrossed loop-like structures, likely originating in plasma confined to magnetic field lines. Based on the new radio image, we carried out a detailed multiwavelength correlation. In the central area, the comparison of the almost simultaneous images confirms that the wisps in the three spectral ranges do not generally coincide in location, the radio emission being the most discordant, which is suggestive of the existence of two different synchrotron components. The X-ray pulsar jet does not have a radio counterpart. Instead, another jet-like feature is seen in radio, though with different curvature and starting point.