  According to the most popular model for the origin of cosmic rays (CRs),
supernova remnants (SNRs) are the site where CRs are accelerated. Observations
across the electromagnetic spectrum support this picture through the detection
of non-thermal emission that is compatible with being synchrotron or inverse
Compton radiation from high energy electrons, or pion decay due to
proton-proton interactions. These observations of growing quantity and quality
promise to unveil many aspects of CRs acceleration and require more and more
accurate tools for their interpretation. Here, we show how multi-dimensional
MHD models of SNRs, including the effects on shock dynamics due to
back-reaction of accelerated CRs and the synthesis of non-thermal emission,
turned out to be very useful to investigate the signatures of CRs acceleration
and to put constraints on the acceleration mechanism of high energy particles.
These models have been used to interpret accurately observations of SNRs in
various bands (radio, X-ray and $\gamma$-ray) and to extract from them key
information about CRs acceleration.
