Modelling relativistic heavy-ion collisions with dynamical transport approaches

We discuss the basic ideas of relativistic transport models used for the interpretation and description of experimental data from heavy-ion collisions at high collision energies. We highlight selected results from microscopic simulations of these reactions with a main focus on the UrQMD and PHSD approaches. We also address the results of macroscopic approaches like hydrodynamics or coarse-grained dynamics used in different model combinations in comparison to experimental data. We address the results of such simulations for the description of QCD matter close to equilibrium in terms of transport coefficients like shear $\eta$ and bulk viscosity $\zeta$ and discuss the connection of the radial flow to the equation of state and the transport properties. Then we turn to dileptons and photons as messengers from the hot and dense region before coming to the exploration of the decoupling stage. Generally, we find that microscopic simulations provide a good description of a large variety of observables over many orders of collision energies.