Consider a random walk {Xn : n≥0} in an elliptic i.i.d. environment in dimensions d≥2 and call P0 its averaged law starting from 0. Given a direction $l\in\mathbb{S}^{d-1}$ , Al={limn→∞ Xn⋅l=∞} is called the event that the random walk is transient in the direction l. Recently Simenhaus proved that the following are equivalent: the random walk is transient in the neighborhood of a given direction; P0-a.s. there exists a deterministic asymptotic direction; the random walk is transient in any direction contained in the open half space defined by this asymptotic direction. Here we prove that the following are equivalent: P0(Al∪A−l)=1 in the neighborhood of a given direction; there exists an asymptotic direction ν such that P0(Aν∪A−ν)=1 and P0-a.s we have $\lim_{n\to\infty}X_{n}/|X_{n}|=\mathbh{1}_{A_{\nu}}\nu-\mathbh{1}_{A_{-\nu}}\nu$ ; P0(Al∪A−l)=1 if and only if l⋅ν≠0. Furthermore, we give a review of some open problems.