© ESO 2015. Aims. In this work, we aim to provide a consistent analysis of the dust properties from metal-poor to metal-rich environments by linking them to fundamental galactic parameters. Methods. We consider two samples of galaxies: the Dwarf Galaxy Survey (DGS) and the Key Insights on Nearby Galaxies: a Far- Infrared Survey with Herschel (KINGFISH), totalling 109 galaxies, spanning almost 2 dex in metallicity. We collect infrared (IR) to submillimetre (submm) data for both samples and present the complete data set for the DGS sample. We model the observed spectral energy distributions (SED) with a physically-motivated dust model to access the dust properties: dust mass, total-IR luminosity, polycyclic aromatic hydrocarbon (PAH) mass fraction, dust temperature distribution, and dust-to-stellar mass ratio. Results. Using a different SED model (modified black body), different dust composition (amorphous carbon in lieu of graphite), or a different wavelength coverage at submm wavelengths results in differences in the dust mass estimate of a factor two to three, showing that this parameter is subject to non-negligible systematic modelling uncertainties. We find half as much dust with the amorphous carbon dust composition. For eight galaxies in our sample, we find a rather small excess at 500 μm (≤1.5σ).We find that the dust SED of low-metallicity galaxies is broader and peaks at shorter wavelengths compared to more metal-rich systems, a sign of a clumpier medium in dwarf galaxies. The PAH mass fraction and dust temperature distribution are found to be driven mostly by the specific star formation rate, sSFR, with secondary effects from metallicity. The correlations between metallicity and dust mass or total-IR luminosity are direct consequences of the stellar mass-metallicity relation. The dust-to-stellar mass ratios of metal-rich sources follow the well-studied trend of decreasing ratio for decreasing sSFR. The relation is more complex for low-metallicity galaxies with high sSFR, and depends on the chemical evolutionary stage of the source (i.e. gas-to-dust mass ratio). Dust growth processes in the ISM play a key role in the dust mass build-up with respect to the stellar content at high sSFR and low metallicity. Conclusions. We conclude that the evolution of the dust properties from metal-poor to metal-rich galaxies derives from a complex interplay between star formation activity, stellar mass, and metallicity.