The understanding of interstellar dust is important in many areas of astrophysics, but its nature, origin, and evolution are still poorly understood. The presence of dust in galaxies has a profound effect on their spectral appearance and on the many processes that determine the physical, chemical, and thermal state of the interstellar medium (ISM). Dust is primarily formed in the ejecta of core collapse supernovae (SNe) and mass outflows of evolved stars, and then subsequently destroyed by SN shocks expanding into the surrounding ISM. I will present the recent progress on the study of SN-formed dust in supernova remnants (SNRs), including recent observations of Cas A, SN 1987A, and the Crab Nebula that revealed significant masses of cold dust, as well as new estimates of global dust destruction rates by SNRs in the Magellanic Clouds. I will discuss the balance between dust formation and destruction by SNe and its implications for dust evolution models and our understanding of the origin of interstellar dust in galaxies.