The approach to studying signs and sign systems, known as modeling systems theory, derives from the work of the Moscow-Tartu School of semiotics. After being largely excluded from mainstream semiotic theory and practice, it is now becoming more and more a major trend in semiotics. The theory envisions a sign structure(or form) as a model of some referent and that the models we make of the world become signs that elicit interpretation of that world. The theory has been applied to the study of biological systems, mathematical cognition, and the origins and development of human cultures. This paper presents an overview of modeling systems theory; differentiation among 'forms', 'signs', and 'models' as separate, yet interrelated, dimensions of semiosis. It describes the features of these dimensions, integrating them into an overall theory of semiosis. The main aim is to synthesize several of the suggestions that the present author has previously put forward in this regard and which refl ect a growing trend in semiotics to revisit basic sign theory in terms of the concept of modeling systems.