In this talk, I will present some recent results on nonparametric analysis of multinomial choice. The first set of results concern identification of Hicksian welfare effects, e.g. compensating variation of price and quality change and introduction/elimination of alternatives. These results can be used to calculate exact cash-equivalents of taxes/subsidies and associated deadweight loss. The second set of results concern the question of integrability, i.e. what restrictions on choice probabilities make them consistent with utility maximization by a heterogeneous population. In applications involving parametric analysis of discrete choice, the latter results inform the choice of functional-forms and out-of-sample predictions of demand, often required for assessing effects of policy changes on consumer demand and welfare.