As innovation increasingly fuels economic growth, higher education institutions and systems face the challenge of equipping students with the skills required by innovative economies. Using two international surveys of tertiary education graduates five years after their graduation, we show that the innovative, tertiary-educated workforce comprises a mix of graduates holding degrees from all disciplines. The contribution to innovation of different graduates varies by type of innovation. When they assess the strong and weak points of their university education, graduates give a mixed picture of the quality of the education they have received. We then link the propensity to participate in innovation to the relative emphasis on theory and practice in university programmes and conclude by highlighting the importance of a competence-based approach to curriculum and pedagogy.