The Skyrme model is a geometric field theory and a quasilinear modification of the nonlinear sigma model, i.e., wave maps into the sphere. In 3+1 dimensions, it is known that this modification prevents self-similar collapse and that global existence holds for large data. I will discuss recent work which demonstrates that this is not the case in 5+1 dimensions. In particular, Skyrme’s modification provides a stable mechanism for finite-time blowup at the self-similar rate.