This paper describes the evolution of the infinitive in terms of its progressive formal and semantic grammaticization, using the German infinitive as an example. It is shown that the infinitive has its diachronic origin in a nominal purposive form and that the grammaticization of a purposive form to an infinitive is a widespread phenomenon in the languages of the world. This original function of the infinitive is important for understanding its nature, and the most interesting syntactic property of infinitive, the absence of an explicit subject, can be shown to follow from it. Finally, this paper shows that the diachronic process of the grammaticization of a purposive form is even more general, occurring also in the case of purposive markers in finite clauses.