The paper presents a comparative analysis of the possibilities and characteristic features of the application of various polyhedral boron compounds, viz., the closo-decaborate anion [B10H10]2–, the closo-dodecaborate anion [B12H12]2–, the carba-closo-dodecaborate anion [CB11H12]–, carboranes C2B10H12, and the bis(dicarbollide) complexes [M(C2B9H11)2]– (M = Fe, Co, or Ni), in boron neutron capture therapy (BNCT) for cancer. The requirements on compounds used in BNCT are formulated and the advantages of the application of the closo-dodecaborate anion are considered. The data on the synthesis of various derivatives of the closo-dodecaborate anion, which either already found use in BNCT or are most promising in this field, are summarized. The possibilities of the application of agents derived from the closo-dodecaborate anion in medical diagnostics are discussed.