Celiac disease (CD) is a complex autoimmune disorder in genetically predisposed individuals of all age groups triggered by the ingestion of food containing gluten. A reliable diagnosis is of high interest in view of embarking on a strict gluten-free diet, which is the CD treatment modality of first choice. The gold standard for diagnosis of CD is currently based on a histological confirmation of serology, using biopsies performed during upper endoscopy. Computer aided decision support is an emerging option in medicine and endoscopy in particular. Such systems could potentially save costs and manpower while simultaneously increasing the safety of the procedure. Research focused on computer-assisted systems in the context of automated diagnosis of CD has started in 2008. Since then, over 40 publications on the topic have appeared. In this context, data from classical flexible endoscopy as well as wireless capsule endoscopy (WCE) and confocal laser endomicrosopy (CLE) has been used. In this survey paper, we try to give a comprehensive overview of the research focused on computer-assisted diagnosis of CD.