Children use syntax to learn verbs, in a process known as syntactic bootstrapping. The structure-mapping account proposes that syntactic bootstrapping begins with a universal bias to map each noun phrase in a sentence onto a participant role in a structured conceptual representation of an event. Equipped with this bias, children interpret the number of noun phrases accompanying a new verb as evidence about the semantic predicate-argument structure of the sentence, and therefore about the meaning of the verb. In this paper, we first review evidence for the structure-mapping account, and then discuss challenges to the account arising from the existence of languages that allow verbs' arguments to be omitted, such as Korean. These challenges prompt us to (a) refine our notion of the distributional learning mechanisms that create representations of sentence structure, and (b) propose that an expectation of discourse continuity allows children to gather linguistic evidence for each verb's arguments across sentences in a coherent discourse. Taken together, the proposed learning mechanisms and biases sketch a route whereby simple aspects of sentence structure guide verb learning from the start of multi-word sentence comprehension, and do so even if some of the new verb's arguments are omitted due to discourse redundancy.