Whether great apes possess the capacity to acquire elements of human language is an enduring scientific question. Over the last 50 years, results from laboratories using either American Sign Language or an artificial symbol-based communication system suggested that core capacities for language acquisition and comprehension are present in apes. After the completion of these projects, newer approaches examining properties of great ape vocalizations and referential gestures have taken up the question. Results from ape language research challenge the claim that human language is a uniquely derived evolutionary specialization, but we are far from reaching consensus on this point. Through these language studies, apes have demonstrated socio-cognitive abilities crucial for the development of language skills, such as joint attention, intersubjectivity, and processing abilities that include referentiality and use of top-down processing for speech restoration. In this chapter, we review ape language projects, the additional work they inspired, and how the results of these studies offer insight into the evolution of language-related cognitive capabilities. We also discuss the effects of enculturation on language acquisition and ethical quandaries that stem from raising apes in homes and laboratories to test hypotheses about the evolution of cognition and language.