We use data from a sample of European higher education graduates at early stages of their working careers to provide evidence on the determinants of the human capital competences (talents, skills and capabilities) acquired by young graduates in Education and of those required by the jobs they perform. More than 36,000 graduates holding a first higher education degree were surveyed about four years after graduation (graduates from 1995 were surveyed in 1999). The data set used examines in detail a number of human capital competences of the graduates and their utilisation on the job, as well as the extent to which the graduates consider their position and tasks linked to their educational careers. Regarding the labour market, both human capital theory, from the supply side, and job competition theory, from the demand side, misses the definition of the links between the competences possessed by higher education graduates and those required by jobs. By looking at realised matches in the labour market, we try to identify those competences associated to graduates' professional success, as well as their determinants and any possible surpluses and shortages of these key competences and their payoffs. Regression techniques are used to gain insight into the labour-market role of those competences generated or promoted through higher education. The following research questions are addressed: What competences are more demanded by jobs performed by young graduates? Do graduates' competences match those required by their jobs? How are competences rewarded in the labour market?