To examine existing definitions of health and health inequalities and to synthesise the most useful of these using explicit rationale and the most parsimonious text.Literature review and synthesis.Existing definitions of health and health inequalities were identified, and their normative properties were extracted and then critically appraised. Using explicit reasoning, new definitions, synthesising the most useful aspects of existing definitions, were created.A definition of health as a structural, functional and emotional state that is compatible with effective life as an individual and as a member of society and a definition of health inequalities as the systematic, avoidable and unfair differences in health outcomes that can be observed between populations, between social groups within the same population or as a gradient across a population ranked by social position are proposed. Population health is a less commonly used term but can usefully be defined to encompass the average, distribution and inequalities in health within a society.Clarifying what is meant by the terms health and health inequalities, and the assumptions, emphasis and values that different definitions contain, is important for public health research, practice and policy.