A probabilistic framework is developed to assess the structural reliability of offshore wind turbines. Probabilistic models are developed to predict the deformation, shear force and bending moment demands on the support structure of wind turbines. The proposed probabilistic models are developed starting from a commonly accepted deterministic model and by adding correction terms and model errors to capture respectively, the inherent bias and the uncertainty in developed models. A Bayesian approach is then used to assess the model parameters incorporating the information from virtual experiment data. The database of virtual experiments is generated using detailed three-dimensional finite element analyses of a suite of typical offshore wind turbines. The finite element analyses properly account for the nonlinear soil-structure interaction. Separate probabilistic demand models are developed for three operational/load conditions including: (1) operating under day-to-day wind and wave loading; (2) operating throughout earthquake in presence of day-to-day loads; and (3) parked under extreme wind speeds and earthquake ground motions. The proposed approach gives special attention to the treatment of both aleatory and epistemic uncertainties in predicting the demands on the support structure of wind turbines. The developed demand models are then used to assess the reliability of the support structure of wind turbines based on the proposed damage states for typical wind turbines and their corresponding performance levels. A multi-hazard fragility surface of a given wind turbine support structure as well as the seismic and wind hazards at a specific site location are incorporated into a probabilistic framework to estimate the annual probability of failure of the support structure. Finally, a framework is proposed to investigate the performance of offshore wind turbines operating under day-to-day loads based on their availability for power production. To this end, probabilistic models are proposed to predict the mean and standard deviation of drift response of the tower. The results are used in a random vibration based framework to assess the fragility as the probability of exceeding certain drift thresholds given specific levels of wind speed.