Despite an increasingly competitive academic market, more and more people are seeking a PhD degree. While significant research focuses on skill attainment during PhD candidature and at PhD exit, we know little about the skills that might be present at PhD entry. We developed a data-driven taxonomy and conducted logistic regressions to analyse selection criteria (listing skills, qualifications, and personal attributes) of 13,562 PhD advertisements posted in 2016-2019 on Euraxess, a European recruitment platform for researchers. We analysed the most prevalent attributes sought for PhD admission, country-based and discipline-specific differences, and changes over time. We find that many of these admission attributes include diverse and transferable skills. Specifically, cognitive, interpersonal skills and personal attributes are trending upwards, and PhD requirements vary significantly by country, discipline and year of posting. We highlight the attributes requested by top 5 countries and top 5 disciplines, and show changes over time. The insights provide guidance for practice, specifically to PhD applicants, early career researchers, and those who support career development. We discuss PhD programmes' alignment and policy implications for pre-doctoral education, redesign of PhD assessment, and improved training provision for students and supervisors.