A detailed global model of atmospheric-pressure He + H2O plasmas is presented in this paper. The model incorporates 46 species and 577 reactions. Based on simulation results obtained with this comprehensive model, the main species and reactions are identified, and simplified models capable of capturing the main physicochemical processes in He + H2O discharges are suggested. The accuracy of the simplified models is quantified and assessed for changes in water concentration, input power and electrode configuration. Simplified models can reduce the number of reactions by a factor of similar to 10 while providing results that are within a factor of two of the detailed model. The simulation results indicate that Penning processes are the main ionization mechanism in this kind of discharge (1-3000 ppm of water), and water clusters of growing size are found to be the dominant charged species when the water concentration is above similar to 100 ppm. Simulation results also predict a growing electronegative character of the discharge with increasing water concentration. The use of He + H2O discharges for the generation of reactive oxygen species of interest in biomedical applications and the green production of hydrogen peroxide are also discussed. Although it would be unrealistic to draw conclusions regarding the efficacy of these processes from a zero-dimensional global model, the results indicate the potential suitability of He + H2O plasmas for these two applications.