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Diet related non-communicable diseases (NCDs), as well as micronutrient deficiencies, are of widespread and growing importance to public health. Authorities are developing programs to improve nutrient intakes via foods. To estimate the potential health and economic impact of these programs there is a wide variety of models. The aim of this review is to evaluate existing models to estimate the health and/or economic impact of nutrition interventions with a focus on reducing salt and sugar intake and increasing vitamin D, iron, and folate/folic acid intake. The protocol of this systematic review has been registered with the International Prospective Register of Systematic Reviews (PROSPERO: CRD42016050873). The final search was conducted on PubMed and Scopus electronic databases and search strings were developed for salt/sodium, sugar, vitamin D, iron, and folic acid intake. Predefined criteria related to scientific quality, applicability, and funding/interest were used to evaluate the publications. In total 122 publications were included for a critical appraisal: 45 for salt/sodium, 61 for sugar, 4 for vitamin D, 9 for folic acid, and 3 for iron. The complexity of modelling the health and economic impact of nutrition interventions is dependent on the purpose and data availability. Although most of the models have the potential to provide projections of future impact, the methodological challenges are considerable. There is a substantial need for more guidance and standardization for future modelling, to compare results of different studies and draw conclusions about the health and economic impact of nutrition interventions.