External representations such as diagrams often appear in teachers' repertoire of pedagogical tools to support students' conceptual learning and problem-solving activities. The study of diagrams and diagrammatic representations has received growing interest from diverse disciplines. Diagrams remain a central feature of science, technology, engineering, and mathematics (STEM) learning areas, in schools and beyond. This study examined teachers' perceptions of diagrams in mathematics, focusing on two aspects. The first was teachers' perceptions on the utility value of diagrams and how they incorporate them in their instructional practice to communicate and make connections between mathematical ideas. The second was teachers' perceptions about their students' use of diagrams in mathematics. An open-ended survey was administered to 20 secondary school (grades 7 to 10) teachers, with at least 3 years of mathematics teaching experience. The findings show that teachers perceived diagrams primarily as a tool for communication of mathematical ideas during instruction. To a lesser extent, they used diagrams to link concepts within and between topics, and as a tool in any part of problem-solving. Some of the challenges they perceived that students may encounter with diagrams were the lack of diagram-specific skills, cognitive demand of constructing diagrams, and less than proficient visuospatial abilities to decode and extract pertinent information. The possible reasons for these findings are discussed with the support of existing literature and inform potential teacher learning programmes and serve as a springboard for future research.