Deep neural models tremendously improved machine translation. In this context, we investigate whether distinguishing machine from human translations is still feasible. We trained and applied 18 classifiers under two settings: a monolingual task, in which the classifier only looks at the translation; and a bilingual task, in which the source text is also taken into consideration. We report on extensive experiments involving 4 neural MT systems (Google Translate, DeepL, as well as two systems we trained) and varying the domain of texts. We show that the bilingual task is the easiest one and that transfer-based deep-learning classifiers perform best, with mean accuracies around 85% in-domain and 75% out-of-domain .