The formation of sulfuric acid-water hydrates in the vapor phase and nucleation rates of sulfuric acid-water clusters are investigated. The result of ab initio calculations and experimental data related to hydrates are utilized to improve the description of sulfuric acid-water hydration and nucleation in atmospheric conditions. The nucleation rates are obtained using the most rigorous nucleation kinetics and the thermodynamically consistent version of the classical nucleation model. The improvements increase the predicted nucleation rates compared to previous models. The predicted nucleation rates are compared with experimental ones, and they are in most cases within experimental errors. Some experimental evidence suggests that the present model gives a more realistic dependence of nucleation rate on relative humidity and sulfuric acid concentration than the earlier versions of the theory.