  We consider a simple random walk (dimension one, nearest neighbour jumps) in
a quenched random environment. The goal of this work is to provide sufficient
conditions, stated in terms of properties of the environment, under which the
Central Limit Theorem (CLT) holds for the position of the walk. Verifying these
conditions leads to a complete solution of the problem in the case of
independent identically distributed environments as well as in the case of
uniformly ergodic (and thus also weakly mixing) environments.
