The cubic nonlinear Schrödinger equation arises in various physical applications and is one of the most fundamental models in dispersive PDEs. In the three dimensional focusing case the formation of singularities via self-similar solutions has been proposed in the 70s by Zakharov in the context of plasma physics. Based on numerical experiments it is now widely believed that there is a self-similar “ground state” solution which appears as an attractor in the time-evolution of generic large initial data. However, the existence of this (or any other finite-energy) self-similar solution has been a long-standing open problem. In this talk, I present recent joint work with Roland Donninger (University of Vienna), which proves, by using mildly computer assisted methods, the existence of a smooth finite-energy self-similar blowup solution to the 3d cubic NLS.