Using a 5s3p contracted Gaussian basis set, with additional d-polarization, s, p, d diffuse and p negative-ion functions, configuration-interaction (CI) methods were applied to the ground state and 55 low-lying states of B2. From the potential curves spectroscopic constants for 53 stable states were obtained. Experimentally, only the 2(3)SIGMA(u)--X (3)SIGMA(g)- system is known. Agreement of calculated with experimental values for the two known states is very good. All-electron CI studies were performed for the two low-lying states X (3)SIGMA(g)- and 1(5)SIGMA(u)-, which are separated by only about 0.14 eV. Relative to the ground state configuration 2-sigma(g)22-sigma(u)21pi(u)2, most excited valence states derive from single and double excitations to 3-sigma(g), 1-pi(u) and 3-pi(g). At higher energies, Rydberg excitations from 1-pi(u) to sigma(u)R, pi(u)R and pi(g)R occur. Perturbations of the A (3)SIGMA(u)--X 3-SIGMA(g)- system, as observed experimentally, were studied. The states most likely to perturb the vibrational levels of X (3)SIGMA(g)- are 1(3)PI(u) and 1(1)SIGMA(g)+, however, they are not allowed as perturbing states by Kronig's selection rules. Although 1(1)SIGMA(g)+ may interact with X (3)SIGMA(g)- via spin-orbit coupling, only vibrational bands with upsilon" greater-than-or-equal-to 8 would be affected. Another explanation of the observed high-upsilon" vibrational levels of the A-X system, identifying the upper state with 1(3)SIGMA(u)-, has been suggested, but this proposal also encounters some difficulties. Comparison of the spectroscopic constants obtained for B2 with theoretical and experimental results for the isovalent molecules Al2 and Ga2 was made. Trends in T(e), omega(e) and R(e) were rationalized on the basis of orbital character.