Proton-boron fusion would offer considerable advantages for the purpose of energy production as the reaction is aneutronic and does not involve radioactive species. Its exploitation, however, appears to be particularly challenging due to the low reactivity of the H-¹¹B fuel at temperatures up to 100 keV. Fusion chain-reaction concepts have been proposed as possible means to overcome this limitation. Relevant findings are reviewed in this article. Energy-amplification processes are also presented, which are of interest for beam-fusion experiments and fast ignition of H-¹¹B fuel. Directions for further work are outlined as well.