Supporting students' mathematical proficiency requires teachers to continuously adapt their instruction in response to their students' instructional needs. To explore what it means to be an adaptive teacher, we conducted a literature review spanning from 1975-2014 of adaptive teaching in mathematics. Using 24 search terms in three databases, we identified 19 articles that met our inclusion criteria. Findings reiterated findings of a previous literature review regarding the importance of: (a) a stimulus, or something to which the teacher must attend; (b) teacher metacognition and reflection, or interpretation and analysis; and (c) teacher action, or response. Additional findings highlighted the importance in mathematics education research to look closely at: (a) how curricula can serve as stimuli aiding adaptive teaching practices; (b) the idea that the teacher reflects directly on the student stimuli, the learning trajectory, or her own actions; and (c) additional teacher responses, including orchestrating classroom discourse, modifying curricular materials, or selecting teaching aids.