Significant experimental and theoretical progress has been made in the U.S. heavy ion fusion program on high-current sources, transport, and focusing. Currents over 200 mA have been transported through a matching section and 10 half-lattice periods with electric quadrupoles. An experiment shows control of high-beam current with an aperture, while avoiding secondary electrons. New theory and simulations of the neutralization of intense beam space charge with plasma in various focusing chamber configurations predict that near-emittance-limited beam focal spot sizes can be obtained even with beam perveance (ratio of beam space potential to ion energy) >10× higher than in earlier HIF focusing experiments. Progress in a new focusing experiment with plasma neutralization up to 10−3 perveance, and designs for a next-step experiment to study beam brightness evolution from source to target are described.