After giving arguments against the claim that the so-called Big Data revolution has made theory building obsolete, the paper discusses the shortcomings of two views according to which there is no rational approach to theory building: the hypothetico-deductive view and the semantic view of theories. As an alternative, the paper proposes the analytic view of theories, illustrating it with some examples of theory building by Kepler, Newton, Darwin, and Bohr. Finally, the paper examines some aspects of the view of theory building as problem solving.