The progressive robotisation and the introduction of artificial intelligence imply economic and social changes. In this paper, we investigate their impact on the occupations of recent Spanish graduates and examine how graduates with different skills can expect their occupations to be transformed by the digital era. To this end --using a three-step approach--we first map occupations in terms of the level of the transformative and destructive effects of digitalization, and determine which groups are most threatened. Second, we characterize the technological occupational groups according to dimensions related to worker and job requirements, such as abilities, skills and tasks performed. Finally, we explore the influence of educational background on the probability of belonging to each group. The analysis relies on three data sources--the main one being microdata from the Survey on Labour Market Insertion of University Graduates (EILU-2019)--which provide exhaustive information about students' education and training during and after their degree. Results show that only about 15% of graduates hold jobs that have a high probability of being replaced by machines over the next 10--20 years, although a significant number will still face changes in their occupations that will affect skill requirements. Graduates working in these occupations will need a high level of flexibility if they are to adjust to rapid changes and not be displaced. Moreover, certain features of students' academic background --such as the field of study or more formal education-- play a key role and offer some tips to mitigate possible disruptions in graduate employability.