Publisher Summary This chapter discusses the continuous work in modern temporal logic, focusing on the philosophical problems that originally inspired Arthur Norman Prior in his pioneering work within temporal logic. The chapter focuses on the philosophical motivation and the various conceptual aspects of the formalisms of modern temporal logic. Construed in this manner, temporal logic turns out to be a nice illustration of how philosophy and mathematical logic can both benefit from a constructive symbiosis. The strength of philosophical logic lies in its self-imposed obligation to take everyday language and common sense reasoning into serious consideration. For this reason, it is natural that the first detailed theory of tenses developed in philosophical logic was based on a study of the grammatical tenses of natural language. However, neither everyday language nor common sense reasoning is unambiguous quantities. They certainly depend on physical and metaphysical assumptions.