This paper examines prospective mathematics teachers' knowledge of asymptotes and asymptotic behaviour of functions in calculus. They are university students and future facilitators of knowledge in upper secondary education. We constructed a "reference epistemological model" to describe the knowledge about asymptotes for upper secondary and university education and explored prospective teachers' relations to targeted knowledge. The study was conducted within the Anthropological Theory of the Didactic as a suitable framework to analyse and interpret knowledge of mathematical notions. Prospective teachers participated in three questionnaires with open, non-routine questions on different aspects of the notion of asymptotes. An analysis showed their knowledge was fragmented and their work relied heavily on algebraic manipulation and memorized formulas from calculus. The results indicated that knowledge of asymptotes and asymptotic behaviour is a potentially powerful context for developing knowledge related to the limits of functions in calculus.