The present era is characterized by increasing interconnectedness and labor automation. These changes raise the need for a new set of skills, often named 21st century skills, which are especially required in science, technology, engineering, and mathematics (STEM) disciplines. Various organizations have recognized the importance of developing these skills; however, studies have found that some STEM higher education institutions have not done enough to foster their students’ 21st century skills. We investigate 21st century skill development in STEM higher education by designing an online questionnaire with senior management at the Technion and administered it to 1,578 participants—939 alumni and 649 final-year students. The questionnaire focused on 14 skills and included open and closed-ended items. We found these skills can be divided into three groups: (1) domain-general thinking skills, (2) soft skills, and (3) STEM-specific skills. Participants perceived the first group of skills to have developed more than the second group, and the second group more than the third. We found participants with a graduate degree perceived their soft skills to have developed more than participants with only an undergraduate degree from the same institution did. Lastly, we identified through content analysis of open responses nine methods of teaching and learning through which all 14 skills had developed. Our analysis shows that complex course assignments, projects, laboratory experiments, and research helped develop more skills than any other method, and particularly soft skills. Our approach, insights and recommendations toward matching 21st century skills with specific methods of teaching and learning may benefit researchers, policy makers, and educators.