Supernova remnants (SNRs) are the outcome of supernovae (SNe, either core-collapse or thermonuclear). The remnant results from the interaction between the stellar ejecta and the ambient medium around the progenitor star. Young SNRs are characterized by strong shocks that heat and ionize the gas, generate magneto-hydrodynamic turbulence, and accelerate particles to relativistic energies. They radiate at all wavelengths, especially in the X-ray domain, where spectro-imaging observations can provide a wealth of information. This paper presents recent progress in the modelling of SNRs, particularly by the means of numerical simulations, and with a focus on three-dimensional aspects. In the first part we will consider SNRs as producers of cosmic rays (CRs). If SNRs are accelerators efficient enough to power the Galactic component of CRs, this must have a visible impact on their dynamics, and therefore on the thermal emission from the plasma, as well as on their non-thermal emission. In the second part we will consider SNRs as probes of the explosion mechanism. The time has come to connect multi-dimensional simulations of SNe and simulations of SNRs, opening the possibility to study the explosion mechanism via the dynamics and morphology of SNRs.
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