A cornerstone in low-dimensional topology is the Nielsen-Thurston Classification Theorem, which provides a blueprint for understanding homeomorphisms of compact surfaces up to homotopy. However, extending this theory to non-compact surfaces of infinite type remains an elusive goal. The complexity arises from the behavior of curves on surfaces with infinite type, which can become increasingly intricate with each iteration of a homeomorphism. To address some of the challenges, we introduce the notion of tame maps, a class of homeomorphisms that exhibit non-mixing dynamics. In this talk, I will present some recent progress on extending the classification theory to such maps. This is joint work with Mladen Bestvina and Federica Fanoni.