In the 80's Grothendieck claimed that general topology was unfit for the study of the shape of geometric objects since it is possible to realise arbitrary wild pathologies within it. He proposed a tame geometry which should not exhibit such phenomena. Around the same time, model theorists interested in a seemingly unrelated question developed the now widely accepted framework of o-minimal structures.
In this talk, I will explain the notion of an o-minimal structure and discuss basic examples of it. I will then continue explaining why they lead to the correct notion of tame geometry. I will finish the talk by sketching applications of o-minimal structures in algebraic geometry.