This paper tests the hypothesis that unions, through imposing wage floors that lead to wage compression, increase on-the-job training. Our analysis focuses on Germany which provides an interesting context to test this hypothesis, due to its large scale apprenticeship programme and its collective bargaining system that is based on voluntary union recognition. To guide the empirical analysis, we first develop a model of firm-financed training. A novel feature of our model is that a unionised and non-unionised sector coexist, and only unionized firms are bound by union wages. The model creates a rich set of empirical implications regarding apprenticeship training, layoffs, wage cuts, and wage compression in unionized and non-unionised firms. Our empirical analysis is based on firm panel data matched with administrative employee data, and provides strong support for our model. Our main results are that unionisation increases training, and that wage floors and wage compression play a more important role in unionised than in non-unionised firms.