Although it accounts only for a small fraction of the baryonic mass, dust has a profound impact on the physical processes at play in galaxies. Thus, to understand the evolution of galaxies, it is essential not only to characterize dust properties per se, but also in relation to global galaxy properties. To do so, we derive the dust properties of galaxies in a volume limited, K-band selected sample, the Herschel Reference Survey (HRS). We gather infrared photometric data from 8 μm to 500μ m from Spitzer, WISE, IRAS, and Herschel for all of the HRS galaxies. Draine & Li (2007, ApJ, 663, 866) models are fit to the data from which the stellar contribution has been carefully removed. We find that our photometric coverage is sufficient to constrain all of the parameters of the Draine & Li models and that a strong constraint on the 20-60μ μm range is mandatory to estimate the relative contribution of the photo-dissociation regions to the infrared spectral energy distribution (SED). The SED models tend to systematically underestimate the observed 500μ μm flux densities, especially for low-mass systems. We provide the output parameters for all of the galaxies, i.e., the minimum intensity of the interstellar radiation field, the fraction of polycyclic aromatic hydrocarbon (PAH), the relative contribution of PDR and evolved stellar population to the dust heating, the dust mass, and the infrared luminosity. For a subsample of gas-rich galaxies, we analyze the relations between these parameters and the main integrated properties of galaxies, such as stellar mass, star formation rate, infraredluminosity, metallicity, Hα and H-band surface brightness, and the far-ultraviolet attenuation. A good correlation between the fraction of PAH and the metallicity is found, implying a weakening of the PAH emission in galaxies with low metallicities and, thus, low stellar masses. The intensity of the diffuse interstellar radiation field and the H-band and Hα surface brightnesses are correlated, suggesting that the diffuse dust component is heated by both the young stars in star-forming regions and the diffuse evolved population. We use these results to provide a new set of infrared templates calibrated with Herschel observations on nearby galaxies and a mean SED template to provide the z = 0 reference for cosmological studies. For the same purpose, we place our sample on the SFR-M* diagram. The templates are compared to the most popular infrared SED libraries, enlightening a large discrepancy between all of them in the 20-100μ μm range. © 2014 ESO.