Cluster models of light nuclei and the method of hyperspherical harmonics: Successes and challenges

Hyperspherical-harmonics method to investigate the lightest nuclei having three-cluster structure is discussed together with recent experiments. Properties of bound states and methods to explore three-body continuum are presented. The challenges created by large neutron excess and halo phenomena are highlighted. Astrophysical aspects of the 7Li + n → 8Li + γ reaction and the solar-boron-neutrinos problem are analyzed. Three-cluster structure of highly excited states in 8Be is shown to be responsible for extreme isospin mixing. Progress in studies of 6He- and 11Li-induced inclusive and exclusive nuclear reactions is demonstrated, providing information on the nature of continuum structures of Borromean nuclei.