This review examines a range of lesson observation frameworks designed for and used in the observation of teaching in mathematics. This includes frameworks specifically designed for international comparisons of teaching practices and teacher effectiveness, as well as those used for teaching development. Five chapters focus on: (1) Introduction (different frameworks for classroom observations; breadth of focus; reliability; validity; and observation frameworks); (2) Tools for the Observation of Effective Teaching (The International System for Teacher Observation and Feedback; the Quality of Teaching Framework; and The Mathematics Education Traditions of Europe Project); (3) The Use of Frameworks for Research in the UK (comparing the three frameworks; (4) Alternative Frameworks (the Knowledge Quartet; Mathematical Quality of Instruction; and Watson's Framework); and (5) Observing to Improve Teaching (observing effective mathematics teaching and observing to develop teaching).