Upper secondary vocational education in Denmark is based on the apprenticeship model, which is recognised as a valuable route to employment for young people, who are not aiming for higher education. However, the apprenticeship model has a major weakness: it does not provide eligibility for higher education. The purpose of this article is to examine this problem in a historical perspective. The article builds on a combination of policy studies, statistical cohort studies and interview studies. First, the article explores why progression from apprenticeship to higher education has become a major policy problem in Denmark. Secondly, it explores political initiatives taken to "build bridges" to higher education. Thirdly, it examines the development of technical higher vocational education, which has been a main destination for the former apprentices. Lastly, it examines changes in the transition patterns from apprenticeships to higher education in recent decades and examines why the transition rate has declined. Explanations for the decline are identified at the structural, the institutional and the individual levels. It concludes by pointing at a dilemma behind the policies pursued: Trying to strengthen the links from apprenticeship to higher education involves a risk of weakening the current strong links to the labour market.