Purpose A fast-changing environment entails several reflections about skills and attitudes required to face the increasing complexity brought by the "glocal, liquid and networked" world in which workers operate (Bauman, 2003; Clarke, 2017). In the literature, an increased attention has been devoted to the impact of interpersonal skills and personal characteristics on employability (Heckman and Kautz, 2012; Succi, 2019; Wheeler, 2016). In this context, the so-called soft skills become of crucial importance, but a lack of academic attention devoted to their development, and a deficit of companies in integrating soft skills in their selection, induction and training processes have been identified (Hurrell, 2016). The paper aims to discuss these issues. Design/methodology/approach An exploratory study has been designed to describe the tools in use to assess soft skills, during the recruitment process and those to develop soft skills of graduates, during their first years on the job. In January 2017, two symmetrical online questionnaires have been sent to 500 HR managers and 240 graduates of a European business school, in Italy and Germany. Findings Results show that graduates and managers describe differently the use of tools to develop graduates' soft skills. The large majority of HR managers indicate they offer formal training to young graduates and that they are involved in the performance appraisal sessions, while only 22 percent of students confirm they receive formal training and only 26 percent declare to be inserted in a performance appraisal process. Moreover, concerning the assessment of soft skills during the selection process, significant differences between Italian and German companies emerged. Research limitations/implications This research constitutes the first step to acknowledge the lack of initiatives devoted to soft skills development, despite their rising importance for the job market. Practical implications Findings allow initiating a discussion about a strategic topic in human resources management: whose responsibility is it to develop soft skills? Should graduates, higher education or companies fill the gap? The study can be extended to other types of higher education institutions, and a qualitative research could deepen the understanding of root causes of the differences identified. Social implications The impact on youth employment, reduction of labor skills mismatch and improvement of managerial practices could be interesting social implications of the study. Originality/value While previous research has predominantly focused on higher education executives and HR managers, this paper's contribution consists in involving young graduates in the reflection on employability.