Transition problems from secondary to tertiary level in mathematics have been a recurrent issue in Sweden. This paper summarises the development during the last decades. Results from two recent research studies that illuminate the transition problem are presented. The first one, based on empirical data from a major Swedish technical university, characterises the widening gap, in content and in approach, between secondary school and first year university courses. The second study deals with students' encounters with mathematical proof and is based on a large investigation at another main Swedish university. We discuss the influence on the current transition problems of school reforms and of the great expansion of higher education in Sweden during the last 10 - 15 years in view of the results from the research studies. (Contains 2 footnotes and 2 figures.)