This paper surveys the theoretical literature on the relationship between income distribution and food demand, and identifies main gaps of current food modelling techniques that affect the accuracy of food demand projections. At the heart of the relationship between income distribution and food demand is Engel's law. Engel's law establishes that as income increases, households' demand for food increases less than proportionally. A consequence of this law is that the particular shape of the distribution of income across individuals and countries affects the rate of growth of food demand. Our review of the literature suggests that existing models of food demand fail to incorporate the required Engel flexibility when (i) aggregating different food budget shares among households; and (ii) changing budget shares as income grows. We perform simple simulations to predict growth in food demand under alternative income distribution scenarios taking into account nonlinearity of food demand. Results suggest that (i) distributional effects are to be expected from changes in between-countries inequality, rather than within-country inequality; and (ii) simulations of an optimistic and a pessimistic scenario of income inequality suggest that world food demand in 2050 would be 2.7 per cent higher and 5.4 per cent lower than distributional-neutral growth, respectively.