Professional Learning Communities (PLC) have been used increasingly in designing and discussing teachers' professional development, but how PLC are organised and framed differ between contexts. There is a lack of meta-level studies that aim to define and compare different ways of organising PLC. In this literature review of 32 studies, Cultural-historical Activity Theory (CHAT) is used as an analytical lens to examine different models for PLC in mathematics. By examining and comparing PLC in mathematics, the review aims to expand understanding of how PLC in mathematics can be organised and framed. The result revealed three distinctive activity systems with different objects: developing norms for collaboration, developing teachers' understanding about mathematics and its teaching, and developing teachers' repertoire of teaching actions. The activity systems vary concerning the use of mediating artifacts and the norms that regulate each activity system, but are similar regarding participants, context, and division of labor. The review indicates that the teachers participating in PLC in mathematics change their norms of collaboration, enhance their understanding of mathematics and its teaching, and/or enhance their ability to design and carry out mathematics teaching. Our findings can assist designers, organisers, participants, and researchers in making informed decisions about PLC in mathematics.