This study explores the competencies that teachers need and it aims at both determining whether teachers currently have them and proposing training strategies that can contribute to achieving them. The research is based on quantitative and qualitative methods, through the use of a survey answered by school leaders (n = 281) along with interviews to some of them (n = 29). The results reveal how today’s schools need teachers who can constantly acquire new competencies, particularly personal and relational ones. Thus, a teacher’s professional development follows a progression in which both social-emotional competencies and sound classroom management are crucial. Other areas of emphasis are joint efforts between schools and universities and the need to consult the educational teams at schools when devising educational policies or designing training plans. We find that teachers partly have these competencies, which has implications for universities and continuing education.