We present global spectral energy distributions (SEDs) from 0.3$\mu$m to 90cm for a sample of seven low-metallicity blue compact dwarf galaxies (BCDs). In addition to data compiled from the literature, we report new SCUBA data for the galaxies in the sample, including the two most metal-poor star-forming galaxies known, IZw18 and SBS0335-052. The standard starburst templates, M82 and Arp220, do not give a good approximation to any of the BCD SEDs in our sample. Several SEDs are instead characterized by: (i) approximately flat radio spectra suggesting dominant thermal processes; (ii) far-infrared (FIR) spectra which peak at or shortward of 60 $\mu$m; (iii) a significant warm dust component and absence of Aromatic Features in Emission (or PAHs) in the mid-infrared (MIR). The SEDs of low-metallicity BCDs do not follow ``canonical'' scaling relations, and the ``standard'' star-formation indicators based on radio continuum, FIR, and MIR luminosities can be discrepant by factors of $\simgt10$. We present new models of the dust SEDs from 5$\mu$m to 1cm, and derive infrared luminosities, dust distributions, temperatures, and masses. The observed SEDs and dust models are interpreted in terms of the active/passive regimes of star formation and trends with metallicity. Finally, we discuss the implications of our results on the $z\simgt6$ starburst populations which will be detected by forthcoming submm and radio facilities.