[Abstract] In this talk we'll discuss self-similar blowup ("focusing") of waves in physical systems. As a benchmark example of a PDE whose solutions display such behaviour, we will examine the nonlinear Schr{\"o}dinger equation (NLS). We 'll review the main wave solutions of the equation and their spectral properties, revealing how they give rise to blowup as the relevant parameters are varied. This effect will then be examined through a general dynamic renormalization point of view that allows one to observe and justify the emergence of focusing solutions. The implications of such a renormalization viewpoint on stability, the normal form of this phenomenon, analogies of the self-similar blowup solutions with travelling wave ones, and generalizations/extensions of this framework will also be briefly discussed. Time permitting, some tantalizing analogies with problems from Bose-Einstein condensation, glasses and even cosmology will be touched upon.