We will talk about the recent progress on localized vortex solutions of incompressible flow, especially for Euler equation and gSQG (generalized surface quasi-geostrophic equation). There are mainly three mathematical method to deal with this topic of PDE: The stream function method, the vorticity method, and the contour dynamics method. Each of these approaches takes several advantages in special aspects of studying the vortex solutions. An introduction of relevant mathematical tools and some recent results via these methods will be given in this talk.