A classical fact is that any two smooth disks with the same boundary in S^3 are isotopic rel. boundary. Many more complicated Seifert surfaces bounded by more interesting knots become isotopic once you push their interiors into the 4-ball. However, it turns out that not all such surfaces become isotopic in B^4. Surprisingly, any two genus-g Seifert surfaces bounded by an alternating knot become isotopic once you push their interiors into the 4-ball. It remains unknown which other knots have this property, or in general how one might count different Seifert surfaces up to isotopy in 4D. In this talk, we’ll talk about classical constructions of interesting Seifert surfaces, how to produce isotopies, and how to obstruct them. This talk is about joint work with Seungwon Kim and Jaehoon Yoo, and also joint work with Kyle Hayden, Seungwon Kim, JungHwan Park, and Isaac Sundberg.