This introduction addresses various aspects of income and wealth inequality and their developments in Germany and the United States. In both countries the distribution of income and wealth has become more unequal during the past decades. We observe some changes in the figures especially for Germany indicating a more unequal situation at present. This holds for both, the income and the wealth inequality measures. Even though redistribution instruments reduce the Gini coefficient for the disposable income compared to the market outcome, there still is an almost steady increasing trend since the middle of the 1980s. Regarding wealth inequality, the ratio of mean to median net wealth reveals values above the OECD average for Germany and the United States. Both, income and wealth inequality are, however, more pronounced in the US.