Significant experimental and theoretical progress has been made in the US heavy ion fusion programme on high-current sources, injectors, transport, final focusing, chambers and targets for high-energy density physics and inertial fusion energy (IFE) driven by induction linac accelerators. One focus of the present research is the beam physics associated with quadrupole focusing of intense, space-charge-dominated heavy ion beams, including gas and electron cloud effects at high currents, and the study of long-distance-propagation effects such as emittance growth due to field errors in scaled experiments. A second area of emphasis in the present research is the introduction of background plasma to neutralize the space-charge of intense heavy ion beams and assist in focusing the beams to a small spot size. In the near future, research will continue in the above areas, and a new area of emphasis will be to explore the physics of neutralized beam compression and focusing to high intensities required to heat targets to high-energy density conditions as well as for IFE.