Four SiO2 polymorphs (alpha-quartz, alpha-cristobalite, alpha-tridymite, and coesite) hare been studied by periodic ab initio methods and by atomistic potentials. The former approach is based on all-electron localized basis sets (atomic orbitals) and on three different Hamiltonians: Hartree-Fock(HF), density functional theory in the local-density approximation (LDA), and density functional theory including gradient corrections (B3-LYP). The semiclassical approach uses interatomic potentials parametrized either on empirical observables or on ab initio theoretical properties. Full structure optimizations have been carried out, and phase transition energies derived; the results are compared with experimental data and with previous theoretical values obtained by plane-wave-pseudopotential techniques. HF and LDA structural results are slightly better than those for B3-LYP, whereas the order of performance is reversed for the relative stability of polymorphs. The quality of semiclassical data is analyzed and discussed.