  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.
