Telemedicine could improve access to medications for opioid use disorder (MOUD). Telemedicine-delivered MOUD (TMOUD) has expanded substantially in response to the restrictions imposed by the COVID-19 pandemic on in-person clinical contact, yet this expansion has not happened consistently across all health systems and countries. This Review aims to understand key factors in TMOUD implementation that might explain variations in uptake. We did a scoping review using three English language databases for articles reporting on the implementation of TMOUD services. 57 peer-reviewed articles were identified, subjected to open coding and thematic analysis, and further interpreted through normalisation process theory (NPT). NPT was originally used to evaluate telehealth innovations and has been applied extensively to describe, assess, and develop the implementation potential of a broad range of complex health-care interventions. By categorising our findings according to the four core NPT constructs of coherence, cognitive participation, collective action, and reflexive monitoring, we aim to rationalise the current evidence base to show the workability of TMOUD in practice. We find that variations in TMOUD models in practice depend on organisations' attitudes towards risk, clinicians' tensions around giving up control over standard practices, organisation-level support in overcoming operational and technological challenges, and evaluation methods that might neglect a potential widening of the digital divide.