The popular distortion or lexicalized reordering models in phrase-based SMT make good local predictions by focusing on reordering on word level, while the synchronous context free grammars in hierarchical phrase-based (HPB) translation models are capable of handling non-local reordering on the translation phrase level.
reordering, especially without any help of external knowledge, remains a great challenge because an accurate reordering is usually beyond these word level or translation phrase level reordering models' ability.