Interstellar dust is a key physical ingredient of galaxies, obscuring star formation, regulating the heating and cooling of the gas, and building-up chemical complexity. In this manuscript, I give a wide review of interstellar dust properties and some of the modern techniques used to study it. I start with a general introduction presenting the main concepts, in molecular and solid-state physics, required to understand the contemporary literature on the subject. I then review the empirical evidence we currently use to constrain state-of-the-art dust models. Follows a long discussion about our current understanding of the grain properties of nearby galaxies, with an emphasis on the results from spectral energy distribution modeling. The following chapter presents dust evolution at all scales. I review the different microphysical evolution processes, and the way they are accounted for in cosmic dust evolution models. I give my take on the origin of interstellar dust in galaxies of different metallicities. The last chapter focusses on methodology. I give an introduction to the Bayesian method and compare it to frequentist techniques. I discuss the epistemological consequences of the two approaches, and show why the field of interstellar dust requires a probabilistic viewpoint. I end the manuscript with a summary of the major breakthroughs achieved in the past decade, and delineate a few prospectives for the next decade.