Résumé en anglais

The purpose of this article is to get mathematicians interested in studying a number of PDEs that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research.