The stochastic dynamics of c and b quarks in the fireball created in nucleus–nucleus collisions at the RHIC and LHC is studied employing a relativistic Langevin equation, based on a picture of multiple uncorrelated random collisions with the medium. Heavy-quark transport coefficients are evaluated within a pQCD approach, with a proper HTL resummation of medium effects for soft scatterings. The Langevin equation is embedded in a multi-step setup developed to study heavy-flavor observables in pp and AA collisions, starting from a NLO pQCD calculation of initial heavy-quark yields, complemented in the nuclear case by shadowing corrections, k T-broadening and nuclear geometry effects. Then, only for AA collisions, the Langevin equation is solved numerically in a background medium described by relativistic hydrodynamics. Finally, the propagated heavy quarks are made hadronize and decay into electrons. Results for the nuclear modification factor R AA of heavy-flavor hadrons and electrons from their semi-leptonic decays are provided, both for RHIC and LHC beam energies.