We consider a curve $alpha$= $alpha$(s) in Minkowski 3-space $E_1^3$ and denote by {T, N, B} the Frenet frame of $alpha$. We say that $alpha$ is a slant helix if there exists a fixed direction U of $E_1^3$ such that the function <N(s)U> is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $E_1^3$.