This paper aims to characterize critical events noticed by novice mathematics teacher-educators (NMTEs) while they facilitate teacher education sessions. Twenty-four NMTEs enrolled in a university course on teaching teachers were asked to facilitate a series of three sessions with preservice teachers, identify critical events from those sessions and analyze these events. Analysis of the 72 critical events reported by the NMTEs yielded a model that can be used to characterize critical events in teacher education sessions (CETEs) and to identify variations within these events. The model comprises three axes: the event participants, the event focus and the dimensions in learning and teaching mathematics (i.e., cognitive, affective and social). The paper discusses the theoretical and empirical construction of the model and demonstrates its potential contribution using examples from our research.