Low-energy boron clusters are characterized by two-dimensional geometry. Aromaticity of these planar boron clusters was established in terms of topological resonance energy (TRE). All planar boron clusters were found to be highly aromatic with large positive TREs even if they have 4n pi-electrons. Aromaticity must therefore be the origin of unusual planar or quasi-planar geometry. Thus, the aromaticity concept is as useful in boron chemistry as it is in general organic chemistry. It is evident that the Huckel 4n + 2 rule of aromaticity should not be applied to such polycyclic pi-systems. Some of the boron clusters are in the triplet electronic state to attain higher aromaticity. Multivalency and electron deficiency of boron atoms are responsible for lowering the energies of low-lying pi molecular orbitals and then for enhancing aromaticity. For polycyclic pi-systems, paratropicity does not always indicate antiaromaticity.