  We consider the Euler equations in ${\mathbb R}^3$ expressed in vorticity
form. A classical question that goes back to Helmholtz is to describe the
evolution of solutions with a high concentration around a curve. The work of Da
Rios in 1906 states that such a curve must evolve by the so-called binormal
curvature flow. Existence of true solutions concentrated near a given curve
that evolves by this law is a long-standing open question that has only been
answered for the special case of a circle travelling with constant speed along
its axis, the thin vortex-rings. We provide what appears to be the first
rigorous construction of {\em helical filaments}, associated to a
translating-rotating helix. The solution is defined at all times and does not
change form with time. The result generalizes to multiple similar helical
filaments travelling and rotating together.
