No one is disputing that Piketty’s books are ground-breaking, that his research and his team’s research are fundamental, or that their databases and reports are invaluable. Moreover, this research puts economics back in history, which is highly commendable. According to Piketty, the relatively egalitarian world of the “Thirty Glorious Years” following the world war II is being replaced by once again very unequal societies, with a force of inertia notably in terms of wealth inequalities. He concludes that the best way to counter this trend is to implement a progressive global capital tax. However, the World Bank, the IMF, multiple academics, Fed surveys, and the US Bureau of Labour Statistics among others have all challenged Piketty’s findings on inequality. The main arguments of the anti-Piketty camp refer to many different fields. Problems with data and methodology, tax cuts, interclass transfers, human capital, liberalisation of the US economy, facts on heritage, the role of private debt, income volatility and the instability of the richest 1% segment are all factors that weaken or disprove Piketty’s findings. The theoretical framework is also debated, especially regarding the three fundamental laws of capitalism: i) the share of capital income in total income equals the rate of return on capital multiplied by the capital income ratio (Law # 1); ii) the rate of growth of national output equals the savings rate out of national output (net of depreciation) divided by the capital-output ratio (Law # 2), and iii) the rate of return on capital systematically exceeds the rate of growth (Law # 3). As a consequence, all Piketty’s recommendations are also under scrutiny. This article is a review of the literature on the main debates around Piketty’s theses.