Abstract In this chapter we study the limit ħ → 0 of quantum mechanics. The passage from quantum mechanics to classical mechanics involves precisely this limit, and the approximation schemes developed for small ħ are known as the semi-classical approximation. The semi-classical approximation has a predecessor: the so-called old quantum theory. Many of the questions concerning the connection between the quantum and classical mechanics were already raised during the years of foundation of quantum mechanics, 1900–1927, but satisfactory answers have not always been obtained.