New nonparametric methods that identify and estimate counterfactuals for individuals, when each is characterized by a vector of unobserved characteristics, are developed and applied to estimate systems of individual consumer demand and welfare measures. The unobserved characteristics are allowed to enter in unrestricted ways. Identification is delivered through two fundamental assumptions: First, the system is invertible in the vector of unobserved heterogeneity. Second, there exist external, individual-specific, covariates that are related to the unobserved heterogeneity and do not enter directly into the system of interest. The observed external variables can be either discrete or continuously distributed. Estimators based on the identifying restrictions are developed and their asymptotic properties derived. Using UK micro data on consumer demand, we apply the methods to estimate individual demand counterfactuals subject to revealed preference inequalities.