Background In constructing or appraising a health economic model, an early consideration is whether the modelling approach selected is appropriate for the given decision problem. Frameworks and taxonomies that distinguish between modelling approaches can help make this decision more systematic and this study aims to identify and compare the decision frameworks proposed to date on this topic area. Methods A systematic review was conducted to identify frameworks from peer-reviewed and grey literature sources. The following databases were searched: OVID Medline and EMBASE; Wiley’s Cochrane Library and Health Economic Evaluation Database; PubMed; and ProQuest. Results Eight decision frameworks were identified, each focused on a different set of modelling approaches and employing a different collection of selection criterion. The selection criteria can be categorized as either: (i) structural features (i.e. technical elements that are factual in nature) or (ii) practical considerations (i.e. context-dependent attributes). The most commonly mentioned structural features were population resolution (i.e. aggregate vs. individual) and interactivity (i.e. static vs. dynamic). Furthermore, understanding the needs of the end-users and stakeholders was frequently incorporated as a criterion within these frameworks. Conclusions There is presently no universally-accepted framework for selecting an economic modelling approach. Rather, each highlights different criteria that may be of importance when determining whether a modelling approach is appropriate. Further discussion is thus necessary as the modelling approach selected will impact the validity of the underlying economic model and have downstream implications on its efficiency, transparency and relevance to decision-makers. Electronic supplementary material The online version of this article (doi:10.1186/s13104-015-1202-0) contains supplementary material, which is available to authorized users.