It is well known that smooth solutions to the 2d Euler equation remain smooth and are globally defined. However the long time behavior of solutions is not well understood. Numerical simulations and physical experiments have shown that coherent structures such as vortices and shears could form naturally and determine the dynamics for very long time. Such coherent structures also appear in three dimensional flows when two dimensional features dominate, e.g., in the formation of hurricanes. In addition, the mechanism of vortex symmetrization near vortices and merging of same sign vortices is fundamental in 2d turbulence. In this talk, we discuss some recent results in rigorously understanding these phenomena on the nonlinear level.