  We study the asymptotic behaviour of random walks in i.i.d. non-elliptic
random environments on $\mathbb{Z}^d$. Standard conditions (and proofs) for
ballisticity and the central limit theorem require ellipticity. We use oriented
percolation and martingale arguments to give non-trivial local conditions for
ballisticity and an annealed invariance principle in the non-elliptic setting.
