Welfare states are important determinants of health. Comparative social epidemiology has almost invariably concluded that population health is enhanced by the relatively generous and universal welfare provision of the Scandinavian countries. However, most international studies of socioeconomic inequalities in health have thrown up something of a public health 'puzzle' as the Scandinavian welfare states do not, as would generally be expected, have the smallest health inequalities. This essay outlines and interrogates this puzzle by drawing upon existing theories of health inequalities--artefact, selection, cultural--behavioural, materialist, psychosocial and life course--to generate some theoretical insights. It discusses the limits of these theories in respect to cross-national research; it questions the focus and normative paradigm underpinning contemporary comparative health inequalities research; and it considers the future of comparative social epidemiology.