Upon what kind of moral order does capitalism rest? Conversely, does the market give rise to a distinctive set of beliefs, habits, and social bonds? These questions are certainly as old as social science itself. In this review, we evaluate how today’s scholarship approaches the relationship between markets and the moral order. We begin with Hirschman’s characterization of the three rival views of the market as civilizing, destructive, or feeble in its effects on society. We review recent work at the intersection of sociology, economics, and political economy and show that these views persist both as theories of market society and moral arguments about it. We then argue that a fourth view, which we call moralized markets, has become increasingly prominent in economic sociology. This line of research sees markets as cultural phenomena and moral projects in their own right, and seeks to study the mechanisms and techniques by which such projects are realized in practice.