Corks are special contractible 4-manifolds that play a key role in the study of exotic smooth 4-manifolds. In this talk, I will describe applications of corks to the study of surfaces in 4-manifolds. I'll begin with some badly behaved 2-spheres in 4-space, based on joint work with Piccirillo. Then I'll use a twist on these ideas to construct smoothly (indeed, holomorphically) embedded disks in the 4-ball that are isotopic through ambient homeomorphisms but not through diffeomorphisms. There will be lots of cartoons.