Much of the evidence about the effects of SNAP on nutrition is based on cross-sectional studies comparing SNAP recipients and eligible non-recipients, and thus potentially biased, even when observables are controlled. There is evidence suggesting SNAP recipients spend more on food than other similar families and that they have higher nutrient availability than others. The lack of good causal evidence is in part due to the many challenges with evaluating what was for most of its life a national program with consistent rules across places, making it impossible to use the most common quasi-experimental estimators. There is also the challenge that any of these comparisons of recipients and non-recipients in standard data sets suffer from misclassification, as SNAP use is underreported. The goal of this paper is to assess the existing state of knowledge about whether SNAP improves health and nutrition outcomes, and if so, which ones and by how much.