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 Alfvénic 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 may be heated at different temperatures (depending on their mass) in the post-shock medium of SNRs. SNRs are also characterized by broadband nonthermal emission stemming from 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 in 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 on the temperatures measured for different ion species in the remnant of the SN observed in 1987 in the Large Magellanic Cloud (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.