  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; $\sim
0.3-0.7 M_{\odot}$ in Type II--P SNe and $\sim 0.13 M_{\odot}$ 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 $\mu$m in Type II-P, and less than 0.006
$\mu$m in Type IIb, which decides the fate of dust in the SNR. The surviving
dust mass is $\sim 0.04-0.2 M_{\odot}$ in the SNRs of Type II--P SNe for the
ambient hydrogen density of $n_{\rm H}=10.0-1.0$ 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.
