Over the last several decades, digital technology (DT) integration in teaching and learning mathematics has received considerable attention, as such integration has not led to the expected results. Teacher education is a critical factor -- even more important than access to tools and devices -- in technology-enhanced teaching and learning. The purpose of this literature review is to examine and systematise core findings of studies that inform mathematics teacher education that supports the integration of digital technologies. We explore key considerations in mathematics teacher education for successfully preparing Prospective Secondary Mathematics Teachers (PSMT) for digital technology integration. This review includes 25 theoretical and empirical articles found using the keywords 'Digital Technology' and 'Mathematics Education'. The review explores different topics that impact teachers' technology integration classified into six categories according to their varying nature: (1) Mathematical digital competence, (2) Empirical and theoretical justifications, (3) Stages in DT integration, (4) Pedagogies for DT integration, (5) Mathematical skills, and (6) Systemic factors. It articulates and connects several findings reported in the extant literature previously seen as isolated and disconnected.