Researchers in the cognitive sciences have long debated the relationships between linguistic input and language structure, as well as the relationships between language and cognition. Homesign systems offer a unique window into these relationships. Homesigns are gesture systems developed by deaf individuals who are not exposed to conventional sign or spoken language input. Homesign systems exhibit a number of linguistic properties, but appear to lack others, which depend on access to a linguistic model and/or interaction within a language community. I will present evidence for structure in homesign from a variety of levels of linguistic analysis, including phonology and discourse structure. I will also discuss the cognitive consequences (or lack thereof) of linguistic (but not social) deprivation, particularly with respect to number cognition. Finally, I will present results suggesting that the linguistic structure in homesign systems is not entirely driven by communication factors.