Anthony Atkinson, Thomas Piketty, and Emmanuel Saez analyze long-term trends in top income shares across 22 countries using income tax data. They find that top income shares fell sharply in the first half of the 20th century due to economic shocks, but did not recover immediately after World War II. Over the last three decades, top income shares have increased significantly in English-speaking countries, India, and China, but not in continental Europe or Japan. This increase is largely due to rising top wage incomes, which now constitute a larger share of top incomes than in the past. The study highlights the importance of top incomes in understanding economic growth, inequality, and global distribution. It also discusses the limitations of tax data, including issues with comparability across countries and time, tax avoidance, and evasion. The authors emphasize the need for further research to understand the factors driving these trends and their implications for public policy. The study provides a comprehensive overview of the methodology, key findings, and open questions in the analysis of top incomes over time.Anthony Atkinson, Thomas Piketty, and Emmanuel Saez analyze long-term trends in top income shares across 22 countries using income tax data. They find that top income shares fell sharply in the first half of the 20th century due to economic shocks, but did not recover immediately after World War II. Over the last three decades, top income shares have increased significantly in English-speaking countries, India, and China, but not in continental Europe or Japan. This increase is largely due to rising top wage incomes, which now constitute a larger share of top incomes than in the past. The study highlights the importance of top incomes in understanding economic growth, inequality, and global distribution. It also discusses the limitations of tax data, including issues with comparability across countries and time, tax avoidance, and evasion. The authors emphasize the need for further research to understand the factors driving these trends and their implications for public policy. The study provides a comprehensive overview of the methodology, key findings, and open questions in the analysis of top incomes over time.