Abstract While machine translation has traditionally relied on large amounts of parallel corpora, a recent research line has managed to train both Neural Machine Translation (NMT) and Statistical Machine Translation (SMT) systems using monolingual corpora only. In this paper, we identify and address several deficiencies of existing unsupervised SMT approaches by exploiting subword information, developing a theoretically well founded unsupervised tuning method, and incorporating a joint re- finement procedure. Moreover, we use our improved SMT system to initialize a dual NMT model, which is further fine-tuned through onthe-fly back-translation. Together, we obtain large improvements over the previous stateof-the-art in unsupervised machine translation. For instance, we get 22.5 BLEU points in English-to-German WMT 2014, 5.5 points more than the previous best unsupervised system, and 0.5 points more than the (supervised) shared task winner back in 2014