Dust extinction and emission are fundamental processes in characterizing the galaxy spectral energy distributions (SEDs) and interpreting multi-band galaxy survey data. However, the evolution of dust properties affecting these processes has not been well understood. This also limits the understanding of observational properties of high-redshift galaxies. In this presentation, we first review the basic dust evolution processes that determine the evolution of extinction curves and SEDs. Next we introduce our recent modeling efforts toward the understanding of dust extinction and emission. In particular, we successfully include the evolution of grain size distribution and grain compositions (including PAHs). We also confirm that the extinction curves and SEDs in nearby galaxies with various metallicities are fairly reproduced. Based on this confirmation, we discuss what our model predicts for the dust properties in high-redshift galaxies. The SED shape is expected to have weak PAH emission in the early phase of galaxy evolution. This explains the correlation between metallicity and PAH emission for a Spitzer sample at z=2.