All solid phases of bismuth under pressure, but one, have been experimentally found to superconduct. From Bi-I to Bi-V, avoiding Bi-IV, they become superconductors and perhaps Bi-IV may also become superconductive. To investigate the influence of the electronic properties N(E) and the vibrational properties F(ω) on their superconductivity we have ab initio calculated them for the corresponding experimental crystalline structures, and using a BCS approach have been able to determine their critical temperatures Tc obtaining results close to experiment: For Bi-I (The Wyckoff Phase) we predicted a transition temperature of less than 1.3 mK and a year later a Tc of 0.5 mK was measured; for Bi-II Tc is 3.9 K measured and 3.6 K calculated; Bi-III has a measured Tc of 7 K and 6.5 K calculated for the structure reported by Chen et al., and for Bi-V Tc ~ 8 K measured and 6.8 K calculated. Bi-IV has not been found to be a superconductor, but we have recently predicted a Tc of 4.25 K.