  Interstellar dust grains play a crucial role in the evolution of the galactic
interstellar medium (ISM). Despite its importance, however, dust remains poorly
understood in terms of its origin, composition, and abundance throughout the
universe. Supernova remnants (SNRs) provide a laboratory for studying the
evolution of dust grains, as they are one of the only environments in the
universe where it is possible to observe grains being both created and
destroyed. SNRs exhibit collisionally heated dust, allowing dust to serve as a
diagnostic both for grain physics and for the plasma conditions in the SNR. I
present theoretical models of collisionally heated dust which calculate grain
emission as well as destruction rates. In these models, I incorporate physics
such as nonthermal sputtering caused by grain motions through the gas, a more
realistic approach to sputtering for small grains, and arbitrary grain
compositions porous and composite grains. I apply these models to infrared and
X-ray observations of Kepler's supernova and the Cygnus Loop in the galaxy, and
SNRs 0509-67.5, 0519-69.0, and 0540-69.3 in the LMC. X-ray observations
characterize the hot plasma while IR observations constrain grain properties
and destruction rates. Such a multi-wavelength approach is crucial for a
complete understanding of gas and dust interaction and evolution. Modeling of
both X-ray and IR spectra allows disentangling of parameters such as pre and
postshock gas density, as well as swept-up masses of gas and dust, and can
provide constraints on the shock compression ratio. Observations also show that
the dust-to-gas mass ratio in the ISM is lower by a factor of several than what
is inferred by extinction studies of starlight. Future observatories, such as
the James Webb Space Telescope and the International X-ray Observatory, will
allow testing of models far beyond what is possible now.
