Self-similar singularities are classical candidates for blowup of nonlinear PDE, and their study has gained tremendous traction in the last decades. In combination with convex-integration techniques, they were used to construct singularities for the forced incompressible Navier-Stokes equations.  We will discuss the most recent developments of the self-similar techniques in the last years, starting with the breakthrough work of Merle, Raphael, Rodnianski and Szeftel for compressible fluids and defocusing supercritical NLS. Then, we will treat incompressible fluids and focusing NLS.