The first generation of theories and computer simulations of liquid crystals have made drastic and often contrasting assumptions on the model representation of constituent mesogens and on the type of intermolecular interactions (e.g purely attractive in Maier-Saupe type and purely hard repulsions in Onsager models). Computer simulations of liquid crystals, that started with simple lattice models, have upgraded over the years to off-lattice models where molecules are replaced by relatively simple objects endowed with attractive and repulsive interactions and, more recently, to very realistic fully atomistic models. In the talk we shall briefly summarize the main features of these models and show various examples for the prediction of liquid crystal phase behavior in the bulk and of alignment and anchoring in thin films starting from various microscopic models. The contribution of different interactions to the phase morphologies obtained as well as open problems will be discussed.