We will give a short overview of the Nielsen-Thurston Classification problem (classifying the homeomorphism type of surfaces) on finite-type surfaces and then move to infinite-type surface mentioning the current state and challenges to extending some known arguments. We will then discuss how current work in progress on potential definitions of pseudo-anosov mapping classes in the infinite-type setting (joint with F.Valdez) and how to address some of the previous challenges (joint with Y.Chandran)