The transition semantics presented in Rumberg (2016) constitutes a novel approach to Prior’s theory of branching time. It has its roots in the peculiar interrelation of actuality and possibility that we find in branching time structures: the forking paths in the tree of possibilities represent temporal alternatives for a dynamic actuality to evolve rather than modal alternatives to a given actuality. In this paper, we discuss the peculiar interrelation of actuality and possibility that is at the heart of the theory of branching time and illustrate how this interrelation is reflected in the transition semantics.