The results of first-principles calculations of the electronic structure and the total energy in strontium bismuth tantalate, SrBi(2)Ta(2)O(9) (SBT), with respect to Ta ion displacements, are reported. In pseudotetragonal SBT and its solid solutions, bismuth oxide, [(Bi(2)O(2))(2+)], layers alternate with double strontium tantalate, [(Sr(2)Ta(2)O(7))(2-)], perovskite layers. The dual crystal chemistries give rise to dual electronic and dielectric properties that are anisotropic. The calculated electronic structure of SBT indicates that the absence of an energy gap in the vicinity of the Fermi level stems from lowering of the Sr orbital energies due to its lower electronegativity relative to Ta and Bi ions, and significant hybridization between Sr, Ta, Bi and O ions. Although charge carriers in the "semimetallic" (Sr(2)Ta(2)O(7))(2-) sublattice have a large effective mass, the (Bi(2)O(2))(2+) sublattice is insulating. The calculated partial and total densities of states provide alternative but plausible explanations to the reported spectroscopic data. The total energy anisotropy indicates that multiple phase transformations, and anisotropies in the polarization retention and coercive field (E(c)), are expected. Explanations of the fatigue-free behavior and leakage current (J(L)) and its anisotropy of SBT, and comments on optical transparency and calculating methods for band structure of SBT are forwarded.