By means of chemical evolution models for galaxies of different morphological type, we have performed a detailed study of the evolution of the cosmic dust properties in different environments: the solar neighbourhood, elliptical galaxies and dwarf irregular galaxies. Starting from the same formalism as developed by Dwek (1998), We have taken into account dust production from low and intermediate mass stars, supernovae II and Ia as well as dust destruction and dust accretion processes in a detailed model of chemical evolution for the solar vicinity. Then, by means of the same dust prescriptions but adopting different galactic models (different star formation histories and presence of galactic winds), we have extended our study to ellipticals and dwarf irregular galaxies. We have investigated how the assumption of different star formation histories affects the dust production rates, the dust depletion, the dust accretion and destruction rates. We have shown how the inclusion of the dust treatment is helpful in solving the so-called Fe discrepancy, observed in the hot gaseous halos of local ellipticals, and in reproducing the chemical abundances observed in the Lyman Break Galaxies. Finally, our new models can be very useful in future detailed spectro-photometric studies of galaxies. ; Comment: 20 pages, A&A, accepted. Minor changes after referee report