What makes a good teacher and what motivates a person to want to teach are timeless questions that concern us all. This study focuses on those who are currently training to become teachers, more specifically undergraduates studying a degree in Primary Education in the universities of Catalonia. It adopts a quantitative methodology based on a self-administered questionnaire conducted with a representative sample. Participants' open-ended responses are recorded and codified. Three main categories are constructed: personal, authentic teacher; the teacher as story teller; and, the teacher as motivator of learning. Results highlight important differences between these categories, extolling above all the authentic, personal teacher, who leaves a mark thanks to their character and way of being. This, together with other findings, raises various considerations for the university training of future teachers.