We study the welfare change from project and policies when consumers' behaviour is described with additive random utility models. We consider the random compensating variation mainstream approach and review the latest methodological developments. The expectation of the random compensating variation is used as a measure of the average welfare change. Without income effect, it is expressed by the monetized difference of the expectations of the maximum utilities with and without the changes in monetary costs or quality. This measure reduces for the multinomial logit model to the logsum formula. More generally, the expectation of the compensating variation can be expressed as a path-independent line integral. The rule-of-a-half is an approximation of this line integral. With income effect, the expectation of the compensating variation, both unconditional and conditional on the choices without and with the changes, is provided by one-dimensional integrals which can be computed numerically. In the conditional case, the average welfare change is attributed to those keeping and those changing alternative. The cumulative distribution function of the compensating variation allows the analysis of inequalities by extending the classical Lorenz curve and Gini coefficient. This analysis is perfomed distinctly for positive and for negative values of the compensating variation. Treatment of observed and unobserved heterogeneity is included. The survey of theoretical results is illustrated with a numerical example in the context of transportation mode choice, based on large-scale data collected in France.