Boron- or Aluminum-rich icosahedral cluster solids (ICS) consist mainly of B12 or Al12 icosahedral clusters. In the ICS, a slight change of the structure or environment of icosahedral cluster can cause metallic-covalent bonding conversion, which can cause that the electrical conductivity σ and the Seebeck coefficient S can be as high as those of metals and semiconductors, respectively. Five-fold symmetry of the icosahedral cluster does not match with the translational symmetry of a crystal, consequently makes lower thermal conductivity κ with complex structure. For these reasons, ICS are promising candidates for thermoelectric materials. In α-AlReSi approximant crystal, the bond strength distributes widely from weak metallic to strong covalent bond, and the intra-cluster bonds are stronger than the inter-cluster ones. This means that α-AIReSi is located at the intermediate state of molecular, metallic- and covalent-bonded solids. Composition dependences of atomic density and quasi-lattice constant for AlPdRe icosahedral quasicrystals show the above situation is the same in the quasicrystals. The thermoelectric figure of merit Z and the effective mass m* of AlPdRe quasicrystals can be increased by strengthening the intra- and weakening the inter-cluster bonds. According to this guiding principle (Weakly Bonded Rigid Heavy Clusters), Z was improved by a factor of 1.5 and 2.0 by substitution of Ru and Fe for Re, respectively. In β-rhombohedral boron, several interstitial sites, which have space large enough to accommodate foreign atoms, are known. For the V doped sample, in which V atoms mainly occupy A1 site, the metallic-covalent bonding conversion may occur, σ is increased very much, S is decreased even to negative value and κ is decreased. The maximum and n-type ZT value is obtained and is approaching to that of B4C, which is considered to have the largest and p-type ZT value in boron-rich ICS.