Of fundamental importance to the study of nonlinear wave equations is the well-posedness of the associated Cauchy problem. While some equations may admit solutions that exist for all time, some equations admit solutions which blow up in finite time. Self-similar solutions provide examples of solutions which are initially smooth and compactly supported yet fail to be continuously differentiable after a finite amount of time. In this talk, we will review developments in the study of stable self-similar blow-up for nonlinear wave equations. After reviewing what is known for a variety of such equations, we will introduce the strong-field Skyrme model. This model is a particular limiting case of the Skyrme model, a quasilinear modification of the nonlinear sigma model (wave maps). We will present recent progress toward establishing the stability of an explicit self-similar solution of the strong-field Skyrme model’s equation of motion. In particular, we will emphasize new challenges due to nonlinear structures absent in previously studied equations.