In the United States, most political jurisdictions are based on geographic districts. After each decennial census, districts must be redrawn to account for changes in population and other demographics. “Gerrymandering” is the process of drawing maps with the intent to give an electoral advantage to a political party or candidate or to disadvantage an ethnic or social population. We describe mathematical and computational tools to detect gerrymandering, measure district characteristics, and generate maps with particular characteristics (including anti-gerrymandering measures such as fairness and competitiveness).