  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)
