This study analyses what kind of conceptions teacher students and engineering students have about the function concept, and how these conceptions differ between the two groups. The study was conducted through questionnaires, and 34 students at a Swedish university participated. The function concepts of the students have been classified according to modified versions of models presented by Vinner & Dreyfus, Sfard and DeMarois & Tall. The result of the study shows that the students primarily have operational concepts of function, with only a couple of students having anything resembling a structural function concept. The study also shows distinct differences between prospective compulsory school teachers and engineering students, where the former have less developed functional concepts.