Aims: Our goal is to determine and study the global emission from the Magellanic Clouds over the full radio to ultraviolet spectral range. Methods: We have selected from the literature those flux densities that include the entire LMC and SMC respectively, and we have complemented these with maps extracted from the WMAP and COBE databases covering the missing 23-90 GHz (13-3.2 mm) and the poorly sampled 1.25-250 THz (240-1.25 μm) spectral ranges in order to reconstruct the global SEDs of the Magellanic Clouds over eight decades in frequency or wavelength. Results: A major result is the discovery of a pronounced excess of emission from the Magellanic Clouds at millimeter and submillimeter wavelengths. We also confirm global mid-infrared (12 μm) emission suppression, and determine accurate thermal radio fluxes and very low global extinctions for both LMC and SMC, the latter being the most extreme in all these respects. Conclusions: These and other dust properties such as the far-UV extinction curve appear to be correlated with (low) metallicity. Possible explanations are briefly considered. As long as the nature of the excess emission is unknown, the total dust masses and gas-to-dust ratios of the Magellanic Clouds cannot reliably be determined