There is a continuing demand to accelerate the development of new materials and optimize the performance of existing ones by use of modeling and simulation combined with critical experiment. For Ti alloys used in structural applications, this involves the development of models that predict the relationships between microstructure and mechanical properties, such as tensile, fatigue, creep and fracture toughness. This paper describes the development of models for the prediction of tensile properties in Ti alloys from a knowledge of microstructure. Optimally, such models would be based on physics-based methods that represent physical reality, i.e., based on mechanistic understanding. Unfortunately, the level of such mechanistic understanding in Ti alloys is not sufficient to encourage such an approach and instead a rules-based campaign has been adopted. Thus, neural networks have been developed based on new databases relating microstructure to properties. This paper describes the combinatorial methods used to generate rapidly the necessary databases, and the performance of both fuzzy-logic and Bayesian neural networks that have been developed using these databases. The accuracy and precision of the predictions afforded by the models will be discussed. Also described will be the way in which these models are being used to perform virtual experiments, where all microstructural features except one of interest (the variable) are held constant permitting the functional dependence of the variable on tensile properties to be determined, and subsequently included in a mechanistically-based model.