We have performed systematic studies of the properties of dust in various environments of nearby galaxies with AKARI. The unique capabilities of AKARI, such as near-infrared (near-IR) spectroscopy combined with all-sky coverage in the mid- and far-IR, enable us to study processing of dust, particularly carbonaceous grains includings polycyclic aromatic hydrocarbons (PAHs), for unbiased samples of nearby galaxies. In this paper, we first review our recent results on individual galaxies, highlighting the uniqueness of AKARI data for studies of nearby galaxies. Then we present results of our systematic studies on nearby starburst and early-type galaxies. From the former study based on the near-IR spectroscopy and mid-IR all-sky survey data, we find that the properties of PAHs change systematically from IR galaxies to ultra- luminous IR galaxies, depending on the IR luminosity of a galaxy or galaxy population. From the latter study based on the mid- and far-IR all-sky survey data, we find that there is a global correlation between the amounts of dust and old stars in early-type galaxies, giving an observational constraint on the origin of the dust.