When interpreting disjunctive sentences of the form ‘A or B’, young children have been reported to differ from adults in two ways. First, children have been reported to interpret disjunction inclusively rather than exclusively, accepting ‘A or B’ in contexts in which both A and B are true (Chierchia et al. 2001; Gualmini et al. 2001). Second, some children have been reported to interpret disjunction conjunctively, rejecting ‘A or B’ in contexts in which only one of the disjuncts is true (Paris 1973; Braine & Rumain 1981; Chierchia et al. 2004; Singh et al. 2015). In this article, we extend the investigation of children's interpretation of disjunction to include both simple and complex forms of disjunction, in two typologically unrelated languages: French and Japanese. First, given that complex disjunctions have been argued to give rise to obligatory exclusivity inferences (Spector 2014), we investigated whether the obligatoriness of the inference would play a role in the acquisition of the exclusive interpretation. Second, using a paradigm that makes the use of disjunction felicitous, we aimed to establish whether the finding of conjunctive interpretations would be replicated for both simple and complex forms of disjunction, and in languages other than English. The main findings from our experiment are that both French- and Japanese-speaking children interpreted the simple and complex disjunctions either inclusively or conjunctively; in contrast, adults generally accessed exclusive readings of both disjunctions. We argue that our results lend further support to the proposal put forth in Singh et al. (2015), according to which the reason some children compute conjunctive meanings while adults compute exclusive meanings is that the two groups differ in their respective sets of alternatives for disjunction. Crucially, adults access conjunction as an alternative to disjunction, and compute exclusive interpretations; in contrast, children access only the individual disjuncts as alternatives, and therefore either interpret the disjunction literally or compute conjunctive inferences. More generally, our findings can be explained quite naturally within recent proposals according to which children differ from adults in the computation of scalar inferences because they are more restricted than adults in the set of scalar alternatives they can access (Barner et al. 2011; Tieu et al. 2015b, among others).