This paper presents the results of the project “21st Century Skills: Changing the Approach to Teaching in Higher Education”, which was funded by the Erasmus+ programme between 2019 and 2021. The study involved seven institutions coming from different parts of Europe; mainly these were universities, but there was also one not-for-profit organisation, and one SME. Past and present-day initiatives and studies relating to the development of soft and digital skills among university students are investigated, with particular regard being paid to their perspective when they first have to face the job market. The study design is threefold, involving firstly desk research, where major documents were collected in Bulgaria, Spain, Turkey, Czech Republic, and Italy; then market research, where a sample of corporate professionals and university representatives were interviewed in order to gather additional information relating to the level of development of these skills among young graduates and employees; and lastly, a comparison between two questionnaires filled in by students before and after completing the courses established by the project. Research stages one and two are briefly introduced, with the main focus of the paper being on stage three and a discussion in which the results from various European countries are compared.  The results reveal that some European countries prioritise some skills more than others. In addition, in the examined countries, it can be seen that 21st Century Skills are still not widely developed by young graduates and there is a mismatch between the value attributed to the improvement of competencies and the actual content of training provided by European universities. In summary, employers and academics have provided key information relating to the most needed skills in the market today. In addition, they have testified that attention should be paid to university projects, such as internship programmes and advanced English courses in order to better prepare young people for the marketplace. Furthermore, students should be more involved in activities aimed at improving their level of 21st Century Skills, with courses specifically designed to address this need and make them more aware of their current skill level and the abilities they are expected to have. Currently, these courses are rarely organised by Higher Education institutions and even when they are, they are not always effective.