This book is designed to highlight the current status and perspectives of application of polyhedral boron compounds and their metal complexes. The main attention is paid to application of polyhedral boron hydrides in medicine including boron neutron capture therapy for cancer, radionuclide diagnostics and therapy, as well as anti-tumour activity of some metal derivatives of carboranes. Boron neutron capture therapy - a binary cancer treatment based upon the interaction of two relatively harmless species, a 10B nucleus and a thermal neutron, which results in the formation of the highly energetic 4He and 7Li as products. These fission products have an effective range of ~10 ìm in tissue, thus, effectively limiting the extent of cellular damage to approximately one cell diameter. Therefore, the selective concentration of boron compounds within the tumour cells, followed by their capturing of thermal neutrons, should result in localised destruction of the malignant cells in the presence of the normal cells. Another possible medical application of polyhedral boron hydrides is radionuclide diagnostics and therapy of cancer, where these compounds can be used for attachment of radionuclide labels to various cancer-targeting biomolecules. Other fields of potential application of polyhedral boron hydrides and their metal complexes are synthesis of new materials (liquid crystals, NLO materials, magnets, semiconductors, etc.), radionuclide extraction from nuclear wastes, ion-selective electrodes, production of thermally stable polymers and high burning composite propellants, development of new catalysts for organic synthesis.