Problem solving is a crucial skill in today’s world that needs to be nurtured in education, particularly in mathematics education. However, teaching problem solving is complex. To get to grips with this complexity, we undertook a systematic literature review to identify the knowledge and skills teachers require to create a learning environment that fosters mathematical problem solving. A literature search on problem solving, mathematics, and teacher knowledge and skills in the databases ERIC, PsycInfo, Scopus, and Web of Science led to a final corpus of 104 articles. These articles were categorized into five categories based on Schoenfeld’s (ZDM Math Educ 52(2):359–376, 2020. ++[https://doi-org.hu.idm.oclc.org/10.1007/s11858-019-01057-5](https://doi-org.hu.idm.oclc.org/10.1007/s11858-019-01057-5)++) teaching for robust understanding (TRU) framework, which we adapted to the context of problem solving: (1) problem-solving skills and knowledge of teaching problem solving, (2) teaching practices to adjust cognitive demand, (3) problem solving for all, (4) students’ active involvement in problem solving, and (5) teacher noticing for problem solving. The findings highlight that the essential knowledge and skills for teaching mathematical problem solving span all dimensions and pose significant challenges for teachers. These results align with existing research on teacher noticing, indicating that teachers’ ability to perceive and interpret students’ work is pivotal in teaching problem solving. Therefore, we suggest to enhance the quality of teaching problem solving through teacher education or professional development programs on teacher noticing within the context of problem solving and on facilitating mathematical discussions in class.
