Braid factorizations provide a link between the braid group and the study of embedded surfaces and complex curves in 4-manifolds. After reviewing a bit of this story, I will explain how quasipositive braid factorizations can help bridge the gap between the rigid complex realm and the exotic smooth setting, building the first examples of complex curves that are isotopic through homeomorphisms but not diffeomorphisms of complex 2-space. Time permitting, I will explain how this relates to a speculative connection between braid factorizations and Khovanov and Floer homologies.