This paper is a review of recent developments of parametric and non-parametric approaches to decompose inequality by subgroups, income sources, causal factors and other unit characteristics. Different methods of decomposing changes in poverty into growth, redistribution, poverty standard and residual components are described. In parametric approaches the dynamics of income accounting for transitory and permanent changes in individual and household earnings conditional of various covariates are also reviewed. Statistical inferences for inequality measurement including delta and bootstrapping and other methods to provide estimates of the sampling distribution are presented. These issues are important in the design of policy measures and expectations about their impacts on earnings inequality and poverty reductions.