Many planar spatially extended systems exhibit localized standing structures such as pulses and oscillons. In particular, such structures can emerge at Turing and forced Hopf bifurcations. In this talk, I will give an overview of these mechanisms and show how geometric blow-up techniques can be used to analyze them: among the findings is the bifurcation of localized structures that have significantly larger amplitudes than expected from formal considerations. This is joint work with Kelly McQuighan, David Lloyd, and Scott McCalla.