Knots live in three-dimensional space, but many fundamental questions about them are four-dimensional: does a knot bound a smoothly embedded disk in the 4-ball, and do distinct spanning surfaces become equivalent there? In this talk, I will discuss two results. First, I will explain why the (2,1)-cable of the figure-eight knot is not smoothly slice. Second, I will describe two minimal-genus Seifert surfaces for the same knot that remain non-isotopic after their interiors are pushed into the 4-ball.