This is a review article of Thomas Piketty's book “Capital in the twenty-first century”. Piketty promotes the old theme that, under capitalism, the rich tend to become richer and the poor become poorer, at least in relative terms. We consider whether the data really shows that wealth and income are becoming more concentrated; the role of income transfers (Piketty's data is for pre-tax and pre-transfer income) and other influences on inequality such as real estate prices; the implications of social and economic mobility; the role of the state in fostering inequality; and the determination of socially acceptable inequality. We conclude that Piketty has not succeeded in showing that the inequality r > g (the rate of return is greater than the rate of growth) is the principal determinant of inequality. Piketty offers neither an accompanying theory of social justice nor a theoretical framework to support his case. In particular, lacking is a revealed appreciation of the effects of high marginal tax rates on growth and efficiency.