Epidemiology has investigated the relationship between health status and different social and economic factors ever since the field emerged. Studies have consistently shown that the population's health status bears a strong social gradient, invariably unfavorable to the less privileged groups. Increasing interest in understanding and characterizing health inequalities has broadened the discussion in the recent literature on appropriate concepts and methodological procedures for measuring differences in health status according to socioeconomic level. This study presents a critical assessment of health inequality indicators, focusing on the following: the redistribution principle and its application to health status; the influence of income inequality; epidemiological and statistical approaches to the problem; and evaluation of health system performance in reducing health inequalities. As an example, inequalities in the neonatal mortality rate are analyzed in the city of Rio de Janeiro, Brazil, 2000, according to the mother's level of schooling, reviewing the minimum requisites for defining an adequate health inequality indicator.