We investigate the charm-quark propagation in the QGP media produced in ultrarelativistic heavy-ion collisions at RHIC and the LHC. Purely collisional and radiative processes lead to a significant suppression of final $D$-meson spectra at high transverse momentum and a finite flow of heavy quarks inside the fluid dynamical evolution of the light partons. The $D$-meson nuclear modification factor and the elliptic flow are studied at two collision energies. We further propose to measure the triangular flow of $D$ mesons, which we find to be nonzero in non-central collisions.