State interventions in markets assume varieties of forms in different economic systems. To capture this variety, we consider state capitalism as a multidimensional concept, first reviewing its historical evolution from both practical and scholarly vantages. We describe several dimensions of state capitalism and demonstrate how cross-national variations can be captured through positioning countries along these dimensions. We use cross-sectional data for a large sample of countries to derive factors that represent key dimensions of state capitalism. We demonstrate how cross-national and historical variation in state capitalism is captured by this Virtual Special Issue and offer suggestions for future research.