The purpose of this article is to investigate the views of university graduates and human resource managers (HRMs) on graduates' employability in terms of the soft skills required by the labour market. Soft skills (personal attributes that enhance an individual's interactions, job performance and career prospects) are necessary in the labour market in addition to hard skills (professional knowledge, tools or techniques). In this study, 178 graduates from the Aristotle University of Thessaloniki and 29 HRMs from Greek companies took part. The research tool was a questionnaire exploring participants' views on the demand for soft skills as a decisive factor in employability. The findings identify differences between the views of the graduates and the HRMs. The graduates tended to overestimate themselves, while the employers argued that graduates lacked the necessary skills. The findings are discussed in relation to the changes needed in higher education institutions and the importance of appropriate interaction and collaboration between companies and universities.