[en] This paper presents a survey of the present theoretical understanding based on advanced analytical and numerical studies of collective processes and beam-plasma interactions in intense heavy ion beams for applications to ion-beam-driven high energy density physics and heavy ion fusion. The topics include: discussion of the conditions for quiescent beam propagation over long distances; and the electrostatic Harris instability and the transverse electromagnetic Weibel instability in highly anisotropic, intense one-component ion beams. In the longitudinal drift compression and transverse compression regions, collective processes associated with the interaction of the intense ion beam with a charge-neutralizing background plasma are described, including the electrostatic electron-ion two-stream instability, the multispecies electromagnetic Weibel instability, and collective excitations in the presence of a solenoidal magnetic field. The effects of a velocity tilt on reducing two-stream instability growth rates are also discussed. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized