Classically, homotopy theories are described using homotopical algebra, e.g. as model categories or (co)fibration categories. Nowadays, they are often formalized as higher categories, e.g. as quasicategories or complete Segal spaces. These two types of approaches highlight different aspects of abstract homotopy theory and are useful for different purposes. Thus it is an interesting question whether homotopical algebra and higher category theory are in some precise sense equivalent. In this talk I will concentrate on cofibration categories and quasicategories. I will discuss some basic features of both notions building up to a result that the homotopy theory of cofibration categories is indeed equivalent to the homotopy theory of cocomplete quasicategories.