Previous work on reference in dialogue has shown that speakers adapt to the concepts that were used in earlier references during an interaction (such as orientation when a dialogue partner describes a chair as “the chair seen from the front”), even if these concepts are generally dispreferred. Here, we investigate to what extent it matters whether speakers interact with an artificial or a human dialogue partner (Study 1) and whether this adaptation indeed takes place at the conceptual level (Study 2). For Study 1 participants interacted either with a computer or with a human confederate and it was found that participants adapt in similar ways and just as much to a human dialogue partner as to a computer. Study 2 used a cross-language interaction paradigm, in which bilingual participants listened to English descriptions after which they had to refer in Dutch (thereby reducing the possibilities for lexical and syntactic alignment). The results showed that even with crosslinguistic prime-target pairings, participants aligned with the attributes used by their dialogue partner, providing further evidence for alignment at the conceptual level.