Studying mathematicians’ work allows researchers to understand the nature of mathematical activity and develop insights about mathematical learning and teaching at the different educational levels. This chapter investigates mathematicians’ perspectives on mathematical curiosity and on its role in their research. Twelve mathematicians, including three from Taiwan, four from Greece, and five from Chile were interviewed using a semi-structured interview. Through thematic analysis four themes of mathematicians’ perspectives of curiosity emerged related to curiosity in general; mathematical curiosity; the development of mathematical curiosity; and the relationship between curiosity and other affect attributes. Concerning the role of mathematical curiosity in mathematician’s research practice four main dimensions emerged: the role of curiosity in different phases of research, in the selection of problems, in the problem-solving process, and in collaboration. The main findings show that mathematical curiosity relates strongly to affective dimensions and that curiosity is an integral part of the research process. Finally, reflections on our findings in relation to the mathematical education of students are included.