Motivated by the problem of symmetric collapsing gas-dynamical shocks we present a scalar toy model that captures blowup of focusing waves. This model is simple enough to allow for explicit calculations, and we study some solutions in detail. As a scalar model it does not describe reflection of waves and this necessitates a new concept of weak solutions. Returning to gas-dynamics we review a part of the extensive literature on compressible flow with symmetry, and collapsing shocks in particular. We outline an approach to study possible blowup for collapsing shocks.