  Supernova remnants (SNRs), the products of stellar explosions, are powerful
astrophysical laboratories, which allow us to study the physics of
collisionless shocks, thanks to their bright electromagnetic emission. Blast
wave shocks generated by supernovae (SNe) provide us with an observational
window to study extreme conditions, characterized by high Mach (and Alfvenic
Mach) numbers, together with powerful nonthermal processes. In collisionless
shocks, temperature equilibration between different species may not be reached
at the shock front. In this framework, different particle species might be
heated at different temperatures (depending on their mass) in the post-shock
medium of SNRs. SNRs are also characterized by a broadband nonthermal emission
stemming at the shock front as a result of nonthermal populations of leptons
and hadrons. These particles, known as cosmic rays, are accelerated up to
ultrarelativistic energies via diffusive shock acceleration. If SNRs lose a
significant fraction of their ram energy to accelerate cosmic rays, the shock
dynamics should be altered with respect to the adiabatic case. This shock
modification should result in an increase of the total shock compression ratio
with respect to the Rankine-Hugoniot value of 4. Here I show that the
combination of X-ray high resolution spectroscopy (to measure ion temperatures)
and moderate resolution spectroscopy (for a detailed diagnostic of the
post-shock density) can be exploited to study both the heating mechanism and
the particle acceleration in collisionless shocks. I report on new results in
the temperatures measured for different ion species in the remnant of SN 1987A.
I also discuss evidence of shock modification recently obtained in the remnant
of SN 1006 a. D., where the shock compression ratio increases significantly as
the angle between the shock velocity and the ambient magnetic field is reduced.
