We will present the conjecture of vortices concentrated around a filament for the 3D Euler equations. While this question is open in general, we will give several geometric configurations where results have been obtained: 2D Euler, axisymmetric 3D Euler without swirl, lake equations and helical 3D Euler without swirl. I will show the link between the kernels of the Biot-Savart law for these equations and for the 2D Euler equations. I will present the main arguments to show the persistence of the concentration towards filaments that move according to the "binormal curvature flow". This work is in collaboration with Martin Donati, Lars Eric Hientzsch and Evelyne Miot.