Observations of supernova remnants (SNRs) by an expanding array of ground-based and
space telescopes have revealed their physical complexity through electromagnetic
radiation over a broad energy range, overwhelming us with a rich variety of
morphological and spectral properties. Young shell-type and middle-aged SNRs can emit
luminous high-energy gamma-rays in GeV and/or TeV, evidencing their roles as efficient
cosmic particle accelerators. Thermal X-ray emission from the shocked ambient material
and expanding ejecta contain valuable information about the circumstellar environments,
the nature of the progenitor stars, and even the explosive nucleosynthesis and matter
mixing processes during the supernova phase. 

I will introduce our numerical model that self-consistently describe the broadband
non-thermal and X-ray thermal emission of SNRs using a hydro calculation, including
physics like non-linear diffusive shock acceleration, non-equilibrium ionization,
various radiative processes, and temperature equilibrations among electrons and ions. We
utilize data from core-collapse and thermonuclear supernova simulations to obtain
compositional and structural data for the supernova ejecta. By following the evolution
of ionization states, temperatures, and dynamics of each ion species in the shocked
plasma, we can synthesize detailed X-ray spectra that can be directly compared with and
make predictions for future spectroscopic data from Astro-H. Simultaneously we compute
the acceleration and evolution of relativistic ions and electrons around the
collisionless shockwaves of SNRs, permitting a coherent calculation of spectra, spatial
distribution and time evolution of broadband non-thermal emission from radio to
gamma-rays. This lets us confront multi-wavelength observational data to provide robust
constraints to the contributions of SNRs of various ages and types to the Galactic
cosmic ray population. For illustration, I will discuss applications of the model to a
few young shell-type and middle-aged SNRs.

I will end the talk by sharing my vision on the future path of theoretical SNR
researches using state-of-the-art numerical simulations and how new telescopes are going
to help us out.