An isoperimetric inequality gives a lower bound on the perimeter of a set in terms of its volume. The task of finding a sharp isoperimetric inequality and characterizing the equality case is called an isoperimetric problem. In Euclidean space, the problem dates back to antiquity, but it took several millennia until a rigorous solution arrived. And this was only the beginning of the story... In this talk, we will start with the classical problem, proceed to some more recent versions, and briefly discuss how the topic of isoperimetry connects various fields ranging from probability theory to computer science.