How to approach the relationship between educational supply and labour market is becoming a severe problem faced by governments, social organizations and education institutions. In this sense, the efforts devoted to the quality of training and education must take into account how to meet the labour market needs, as well as the social needs. Economic growth and citizens' progress are at the basis of the future development through education and training, that is the reason why the quality of training and education cannot forget the labour market needs. There is a basic consensus that the 21st century education must be transformed by assuming new roles and committing to economic and social development. To do so, a dynamic social and productive model based on knowledge is needed to forge the innovation necessary to boost competitiveness and economic growth. In this context, competency-based education has experienced a growing interest in the last decades. Since then, numerous studies have focused on the analysis of the skills graduate students should have acquired. Several of them show that the type and level of skills acquired by graduates tend to be lower than the required for the job. This paper explores the idea of competences through the internships last-year undergrad students carry out in firms as their first contact to labour market. It aims at analysing to which extent they fit into the firms' requirements. To do so we use data from a survey conducted amongst the firms' supervisors of 192 students granted the Santander fellowship during the 2015-16 academic year. The database covers all University of Barcelona Schools. The survey consisted of 35 questions, 10 of them referring to the explicit assessment of each of the 38 competences analysed from two points of view (required and observed) and grouped into the three standard blocks: instrumental, interpersonal and professional. The principal components multivariate analysis is applied to analyse the competencies favouring success in entering the labour market. The multivariate analysis allows us to reduce the dimensionality of the variables under study, contributing to identify the aspects that summarize and group the 38 competencies studied from the required firms' perspective into 4 factors: knowledge, operational, understanding the environment and interaction. On the contrary, the analysis from the observed perspective groups them into three factors: knowledge, interaction and management. The results shows the need for professionals who are able to communicate their ideas, work both autonomously and as a team, apply knowledge to practice, search and manage information, have continuous learning capacity, and analyse and solve problems. This requires practically oriented training processes in order to meet the society future needs, focused on versatility, flexibility and adaptability. The rapprochement to these needs will certainly favour graduates' employability.