Core-collapsed supernovae (CCSNe) have been considered to be one of sources of dust in the universe. What kind and how much mass of dust are formed in the ejecta and are injected into the interstellar medium (ISM) depend on the type of CCSNe, through the difference in the thickness (mass) of outer envelope. In this review, after summarizing the existing results of observations on dust formation in CCSNe, we investigate formation of dust in the ejecta and its evolution in the supernova remnants (SNRs) of Type II–P and Type IIb SNe. Then, the time evolution of thermal emission from dust in the SNR of Type IIb SN is demonstrated and compared with the observation of Cas A. We find that the total dust mass formed in the ejecta does not so much depend on the type; ∼0.3–0.7 Msun in Type II–P SNe and ∼0.13 Msun in Type IIb SN. However the size of dust sensitively depends on the type, being affected by the difference in the gas density in the ejecta: the dust mass is dominated by grains with radii larger than 0.03 μm in Type II-P, and less than 0.006 μm in Type IIb, which decides the fate of dust in the SNR. The surviving dust mass is ∼0.04&emdash;0.2 Msun in the SNRs of Type II–P SNe for the ambient hydrogen density of nH=10.0–1.0 cm-3 while almost all dust grains are destroyed in the SNR of Type IIb. The spectral energy distribution (SED) of thermal emission from dust in SNR well reflects the evolution of dust grains in SNR through erosion by sputtering and stochastic heating. The observed SED of Cas A SNR is reasonably reproduced by the model of dust formation and evolution for Type IIb SN. Cosmic Dust - Near and Far. 8-12 September 2008. Convention Center, Heidelberg, Germany.