The article puts forward a branching - style framework for the analysis of determinism and indeterminism of scientific theories, starting from the core idea that an indeterministic system is one whose present allows for more than one alternative possible future. We describe how a definition of determinism stated in terms of branching models supplements and improves current treatments of determinism of theories of physics. In these treatments, we identify three main approaches: one based on the study of (differential) equations, one based on mappings between temporal realizations, and one based on branching models. We first give an overview of these approaches and show that current orthodoxy advocates a combination of the mapping- and the equations - based approaches. After giving a detailed formal explication of a branching - based definition of determinism, we consider three concrete applications and end with a formal comparison of the branching- and the mapping-based approach. We conclude that the branching - based definition of determinism most usefully combines formal clarity, connection with an underlying philosophical notion of determinism, and relevance for the practical assessment of theories.