This dissertation explores the role of epistemic reasoning (i.e., reasoning about other people's knowledge, beliefs, and intentions) in implicature computation by addressing two seeming paradoxes: first, the fact that typically- developing children fail at specific inferences known as scalar implicature until relatively late in development despite exhibiting basic epistemic reasoning abilities from an early age, and, second, the fact that individuals with Autism Spectrum Disorders (ASD) have been claimed to succeed at scalar implicature despite exhibiting deficits with epistemic reasoning in other domains. Chapter 2 provides evidence that 5-year-olds successfully compute ignorance implicatures - inferences that involve significant epistemic reasoning about speaker knowledge and utterance informativeness - despite failing to compute scalar implicatures. On the basis of this finding, we argue that children's failures with scalar implicature do not stem from any difficulty with the epistemic reasoning involved and, instead, are most likely due to an inability to access the specific lexical alternatives involved in scalar implicature. Results from Chapter 2 also show that 4-year-olds fail to compute both ignorance and scalar implicature, suggesting that the ability to compute basic Gricean inferences in language emerges around 5 years of age. This finding is somewhat at odds with claims in the literature that children can compute other forms of pragmatic inference such as ad hoc implicatures at an earlier age. Chapter 3 therefore explores the role of epistemic reasoning in children's ability to compute ad hoc implicatures. We show that 4-year-olds successfully compute ad hoc implicatures despite failing to compute ignorance implicatures, which raises the possibility that children compute ad hoc implicatures before they are able to engage in epistemic reasoning about speaker knowledge and utterance informativeness. Finally, chapter 4 tests epistemic reasoning abilities in high-functioning children and adolescents with ASD. Results show that high- functioning adolescents with ASD successfully compute both scalar and ignorance implicature, while younger children with ASD fail at both inferences. These results indicate that high-functioning individuals with ASD are capable of the kind of epistemic reasoning required to make basic inferences in language despite their other pragmatic deficits, although this ability nevertheless appears to be somewhat delayed in ASD