We review recent theoretical studies on ion diffusion in (Li(2)O)(x)(B(2)O(3))(1-x) compounds and at the interfaces of Li(2)O :B(2)O(3) nanocomposite. The investigations were performed theoretically using DFT and HF/DFT hybrid methods with VASP and CRYSTAL codes. For the pure compound B(2)O(3), it was theoretically confirmed that the low-pressure phase B(2)O(3)-I has space group P3(1)21. For the first time, the structure, stability and electronic properties of various low-index surfaces of trigonal B(2)O(3)-I were investigated at the same theoretical level. The (101) surface is the most stable among the considered surfaces. Ionic conductivity was investigated systematically in Li(2)O, LiBO(2), and Li(2)B(4)O(7) solids and in Li(2)O:B(2)O(3) nanocomposites by calculating the activation energy (E(A)) for cation diffusion. The Li(+) ion migrates in an almost straight line in Li(2)O bulk whereas it moves in a zig-zag pathway along a direction parallel to the surface plane in Li(2)O surfaces. For LiBO(2), the migration along the c direction (E(A) = 0.55 eV) is slightly less preferable than that in the xy plane (E(A) = 0.43-0.54 eV). In Li(2)B(4)O(7), the Li(+) ion migrates through the large triangular faces of the two nearest oxygen five-vertex polyhedra facing each other where E(A) is in the range of 0.27-0.37 eV. A two-dimensional model system of the Li(2)O :B(2)O(3) interface region was created by the combination of supercells of the Li(2)O (111) surface and the B(2)O(3) (001) surface. It was found that the interface region of the Li(2)O:B(2)O(3) nanocomposite is more defective than Li(2)O bulk, which facilitates the conductivity in this region. In addition, the activation energy (E(A )) for local hopping processes is smaller in the Li(2)O :B(2)O(3) nanocomposite compared to the Li(2)O bulk. This confirms that the Li(2)O:B(2)O(3) nanocomposite shows enhanced conductivity along the phase boundary compared to that in the nanocrystalline Li(2)O.