We provide a suggestive examination of state of knowledge on measurement and analysis of ‘inequality’ of outcomes, especially of incomes and earnings. This perspective aims to describe the state of art techniques for identifying the distribution of outcomes as the central object and consider interesting functions of it, such as inequality measures, poverty and mobility indices. We distinguish between ‘scalar’, cardinal functions such as indices, as well as weak uniform rankings, such as by stochastic dominance based on modern rigorous tests. A basic theme permeates the discussion, that of decision theoretic foundations within the potential outcomes paradigm. This permits connectivity and advancement of knowledge that is policy relevant, reveals the essential subjectivity of indices and assessments, and allows important consideration of counterfactual distribution of outcomes. Identification of distributions and their functionals exposes the impact of covariates and different contributing factors to outcomes. A recurrent example is the distribution of earnings of different groups within a population, and decomposition of outcomes by group or other characteristics, and counterfactual states. Modern foundations of inequality measures, dominance rankings, quantile differences/effects, as well as quantile models, instrumental variables and ‘distribution regressions’ are included and analyzed. The hope is to encourage and facilitate adoption of these important new developments at a time of heightened interest in this central socio-political area of policy analysis. The closely related notions of multivariate well being, mobility and poverty, merit separate treatment and are not addressed.