ABSTRACT We study the dust evolution in galaxies by implementing a detailed dust prescription in the SAGE semi-analytical model (SAM) for galaxy formation. The new model, called Dusty SAGE, follows the condensation of dust in the ejecta of Type II supernovae and asymptotic giant branch stars, grain growth in the dense molecular clouds, destruction by supernovae shocks, and the removal of dust from the interstellar medium (ISM) by star formation, reheating, inflows, and outflows. Our model successfully reproduces the observed dust mass function at redshift z = 0 and the observed scaling relations for dust across a wide range of redshifts. We find that the dust mass content in the present Universe is mainly produced via grain growth in the ISM. By contrast, in the early Universe, the primary production mechanism for dust is the condensation in stellar ejecta. The shift of the significant production channel for dust characterizes the scaling relations of dust-to-gas (DTG) and dust-to-metal (DTM) ratios. In galaxies where the grain growth dominates, we find positive correlations for DTG and DTM ratios with both metallicity and stellar mass. On the other hand, in galaxies where dust is produced primarily via condensation, we find negative or no correlation for DTM and DTG ratios with either metallicity or stellar mass. In agreement with observation showing that the circumgalactic medium contains more dust than the ISM, our model also shows the same trend for z < 4. Our SAM is publicly available at https://github.com/dptriani/dusty-sage.