Problem solving has been a prominent field of research in mathematics education for several decades; however, it is still a current trend, due to the relevance of this theme in the teaching and learning of mathematics, across all grade levels and around the world. The importance of problem solving has taken on new contours, either by being considered as a central element of mathematical literacy and competence, or by the recommendations of its cross-curricular integration. Further, problem solving is constantly being mentioned as a highly valued 21st century skill, along with others like creativity, critical thinking, communication or collaboration. Parallel to problem solving comes problem posing. It is a more recent field of research, still in deep development, that has strong connections with creativity and critical thinking. Despite advances in research on mathematical problem solving, new questions and contexts arise that justify further investigation, such as challenges for (future) teachers and students; problem posing; creativity; articulation with other abilities; connections with other disciplinary areas; formal vs. nonformal education; relation with technology; and articulation with the affective domain.