Fusion reactors as presently conceived are breeders of tritium and, possibly, plutonium as well; a single reactor produces hundreds of tons of radioactive waste per year. Comparatively clean fusion fuels which avoid the production of radioactive matter are reviewed, together with the physical concepts how these fuels can be burnt. The main problems are bremsstrahlung and ion cooling in the presence of electrons, and low power density in the absence of electrons. Laser compression of pellets of a mixture of protons and boron-11 may be a solution when lasers in the megajoule range become available. Other valuable research and development efforts are clamped beam-plasma devices, the Migma cell, and direct converters.