Objective: To systematically review the potential impact of reducing the set of Supplemental Nutrition Assistance Program (SNAP)-eligible foods (e.g. not allowing purchase of sugar-sweetened beverages with SNAP benefits) on expenditures for restricted foods. Design: The impact on food expenditures of a $US 1 reduction in available SNAP benefits can be used to estimate the impact of restrictions on SNAP-eligible foods. An electronic search of EconPapers, AgEcon Search, EconLit, WorldCat, ProQuest Dissertations and Theses, PubMed and NALDC, and a snowball search were conducted to obtain a sample of studies up to March 2015 that estimate the impacts of SNAP and other income on household food expenditures. The studies were classified according to study population, study design and whether they attempted to correct for major study design biases. Setting: Estimates were extracted from fifty-nine published and unpublished studies. Subjects: US households. Results: Fifty-nine studies were found, yielding 123 estimates of the impact of SNAP benefits on food expenditures and 117 estimates of the difference in impacts between SNAP benefits and other income. Studies correcting for or mitigating study design biases had less estimate variation. Estimates indicate that expenditures on the restricted item would decrease by $US 1·6 to $US 4·8 if $US 10 of SNAP benefits would have otherwise been spent, with a median overall impact of $US 3. Conclusions: The present literature suggests that restrictions on SNAP-eligible items may result in a small but potentially meaningful decrease in SNAP expenditures for restricted items. Further research is needed to evaluate whether this would translate into improvements in diet quality. Some studies have shown that participants in the Supplemental Nutrition Assistance Program (SNAP) suffer more from obesity than non-participants (1,2) , possibly due to poor diet quality (3) . Policy proposals to address these issues typically consist of either incentivizing healthier food options (4) or restricting the set of foods that can be bought with benefits (5) . The effectiveness and impact of restrictions, however, is a subject of considerable debate. Whether restrictions will actually lead to a decrease in purchasing and consumption of restricted foods depends on how much a decrease in SNAP purchasing power leads to a corresponding decrease in food expenditures. An individual may simply decide to offset the decrease in SNAP purchasing power by using other income to purchase any restricted items. Thus, the extent to which SNAP participants are willing to substitute other income for SNAP income determines the ability of restrictions to reduce purchasing of restricted foods.Over fifty studies, appearing between 1974 and 2014 and using a variety of methods, have estimated the extent of this substitution. However, the most recent review of this literature included studies only up to 2001 (6) . Additionally, that review as well as earlier reviews (7)(8)(9) did not undertake a comprehensive search...