Heavy-flavour observables in relativistic nuclear collisions: theory overview

Transport calculations represent the major tool to simulate the modifications induced by the presence of a hot-deconfined medium on the production of heavy-flavour particles in high-energy nuclear collisions. After a brief description of the approach and of the major achievements in its phenomenological applications we discuss some recent developments. From the theory side we focus on the evaluation of transport coefficients and on recent formulations of the problem of heavy-flavour in-medium propagation in the language of open quantum systems. From a more phenomenological perspective we give an overview of the attempts to extend theoretical models to reproduce recent experimental data arising from event-by-event fluctuations (odd flow harmonics, event-shape-engineering) or from medium-modifications of hadronization ($D_s$ and $\Lambda_c$ production)