A recent literature has constructed top income shares time series over the long run for more than twenty countries using income tax statistics. Top incomes represent a small share of the population but a very significant share of total income and total taxes paid. Hence, aggregate economic growth per capita and Gini inequality indexes are sensitive to excluding or including top incomes. We discuss the estimation methods and issues that arise when constructing top income share series, including income definition and comparability over time and across countries, tax avoidance, and tax evasion. We provide a summary of the key empirical findings. Most countries experience a dramatic drop in top income shares in the first part of the twentieth c...