Noticing is a crucial part of any teachers' classroom practices. Given its importance, research in teacher noticing has gained traction and has significantly increased in recent years. In this survey paper, we explore the terrains of research on teacher noticing in three areas: conceptualisations of teacher noticing, methodological approaches for studying teacher noticing, and contexts within which studies of teacher noticing are situated. We synthesize emerging ideas and insights by contributing authors along these strands to describe the current state of teacher noticing research and papers included in this special issue (2021-1) of "ZDM--Mathematics Education" and conclude by raising questions to chart future directions for research.