Context. In critical domains, assurance corresponds to the set of activities to provide confidence that a system can be deemed dependable, e.g., safe and secure. This essential system and software engineering process is usually conducted according to standards. For novel applications running at the edge and using artificial intelligence (AI), how to conduct assurance in a systematic way is still under study.Objective. The goal of this paper is to provide a comprehensive understanding of current Edge AI assurance considerations. Our interest lies in contributing insights that offer a forward-looking perspective on what is essential in this research field.Method. We conducted a systematic mapping study (SMS) to characterize how Edge AI assurance is addressed in existing literature. The SMS was built on 38 studies, selected through a multi-stageprocess, from 3113 studies published between 2019 and 2025. The 38 studies were deeply analysed focusing on seven research questions about the main key Edge AI assurance aspects: dependabilityconcerns, application domains, assurance standards, assurance evidence, dependability justification techniques, and edge and AI characteristics.Results. We found ten dependability concerns that have been addressed (e.g., safety and security), six application domains (e.g., Industry 4.0), eight assurance standards and regulations (e.g., ISO 26262),27 types of assurance evidence (e.g., architecture specification), three dependability justification techniques (e.g., argumentation), five AI-specific characteristics (e.g., machine learning algorithms)and five edge-specific characteristics (e.g., network).Conclusions. The paper is, to our knowledge, the only existing review on the topic of Edge AI assurance. The results are relevant to practitioners seeking a better grasp on this field as well as researchers to find new research gaps. We have also identified research areas where more effort can be undertaken (e.g., multi-concern assurance).