Every knot leaves a trace in the 4-dimensional world. The trace of a knot is the smooth $4$-manifold obtained by attaching a $2$-handle to the $4$-ball along a knot in the $3$-sphere. We will carefully introduce the relevant notions and discuss a recent strategy due to Manolesu-Piccirillo to disprove the smooth Poincar\'e conjecture by finding knot traces with certain exotic properties. In the second part of the talk, we will explain a method to search for such exotic knot traces, as indicated in the picture. This is based on joint work in progress with Nicolas Weiss.