We have mapped out the complete phase diagram of hard spherocylinders as a function of the shape anisotropy L/D. Special computational techniques were required to locate phase transitions in the limit L/D→∞ and in the close-packing limit for L/D→0. The phase boundaries of five different phases were established: the isotropic fluid, the liquid crystalline smectic A and nematic phases, the orientationally ordered solids - in AAA and ABC stacking - and the plastic or rotator solid. The rotator phase is unstable for L/D ≥ 0.35 and the AAA crystal becomes unstable for lengths smaller than L/D≈7. The triple points isotropic-smectic-A-solid and isotropic-nematic-smectic-A are estimated to occur at L/D = 3.1 and L/D = 3.7, respectively. For the low L/D region, a modified version of the Gibbs-Duhem integration method was used to calculate the isotropic-solid coexistence curves. This method was also applied to the I-N transition for L/D>10. For large L/D the simulation results approach the predictions of the Onsager theory. In the limit L/D →∞ simulations were performed by application of a scaling technique. The nematic-smectic-A transition for L/D →∞ appears to be continuous. As the nematic-smectic-A transition is certainly of first order nature for L/D≤5, the tri-critical point is presumably located between L/D=5 and L/D=∞. In the small L/D region, the plastic solid to aligned solid transition is first order. Using a mapping of the dense spherocylinder system on a lattice model, the initial slope of the coexistence curve could even be computed in the close-packing limit.