BackgroundExternal evidence is commonly used to inform survival modeling for health technology assessment (HTA). While there are a range of methodological approaches that have been proposed, it is unclear which methods could be used and how they compare.PurposeThis review aims to identify, describe, and categorize established methods to incorporate external evidence into survival extrapolation for HTA.Data SourcesEmbase, MEDLINE, EconLit, and Web of Science databases were searched to identify published methodological studies, supplemented by hand searching and citation tracking.Study SelectionEligible studies were required to present a novel extrapolation approach incorporating external evidence (i.e., data or information) within survival model estimation.Data ExtractionStudies were classified according to how the external evidence was integrated as a part of model fitting. Information was extracted concerning the model-fitting process, key requirements, assumptions, software, application contexts, and presentation of comparisons with, or validation against, other methods.Data SynthesisAcross 18 methods identified from 22 studies, themes included use of informative prior(s) (n= 5), piecewise (n= 7), and general population adjustment (n= 9), plus a variety of “other” (n= 8) approaches. Most methods were applied in cancer populations (n= 13). No studies compared or validated their method against another method that also incorporated external evidence.LimitationsAs only studies with a specific methodological objective were included, methods proposed as part of another study type (e.g., an economic evaluation) were excluded from this review.ConclusionsSeveral methods were identified in this review, with common themes based on typical data sources and analytical approaches. Of note, no evidence was found comparing the identified methods to one another, and so an assessment of different methods would be a useful area for further research.HighlightsThis review aims to identify methods that have been used to incorporate external evidence into survival extrapolations, focusing on those that may be used to inform health technology assessment.We found a range of different approaches, including piecewise methods, Bayesian methods using informative priors, and general population adjustment methods, as well as a variety of “other” approaches.No studies attempted to compare the performance of alternative methods for incorporating external evidence with respect to the accuracy of survival predictions. Further research investigating this would be valuable.