The ability to communicate, functionally, after stroke or other types of acquired brain injury is crucial for the person involved and the people around them. Accordingly, assessment of functional communication is increasingly used in large-scale randomized controlled trials as the primary outcome measure. Despite the importance of functional communication abilities to everyday life and their centrality to the measured efficacy of aphasia interventions, there is little knowledge about how commonly-used measures of functional communication relate to each other, whether they capture and grade the full range of patients’ remaining communication skills and how these abilities relate to the patients’ verbal and nonverbal impairments as well as the underpinning lesions. Going beyond language-only factors is essential given that nonverbal abilities can play a crucial role in an individual’s ability to communicate effectively. The current study, based on a large sample of patients covering the full range and types of poststroke aphasia, addressed these important, open questions. The investigation combined data from three established measures of functional communication (ANELT, Scenario Test, COAST) with a thorough assessment of verbal and nonverbal cognition as well as structural neuroimaging. The key findings included: (a) due to floor or ceiling effects, the full range of patients’ functional communication abilities was not captured by a single assessment alone, limiting the utility of adopting individual tests as outcome measures in randomized controlled trials; (b) phonological abilities were most strongly related to all measures of functional communication; and (c) nonverbal cognition was particularly crucial when language production was relatively impaired and other modes of communication were allowed, when patients rated their own communication abilities, and when carers rated patients’ basic communication abilities. Finally, in addition to lesion load being significantly related to all measures of functional communication, lesion analyses showed partially overlapping clusters in language regions for the functional communication tests. Moreover, mirroring the findings from the regression analyses, additional regions previously associated with nonverbal cognition emerged for the Scenario Test and for the Patient COAST. In conclusion, our findings elucidated the cognitive and neural bases of functional communication abilities, which may inform future clinical practice regarding assessments and therapy. In particular, it is necessary to use more than one measure to capture the full range and multifaceted nature of patients’ functional communication abilities and a therapeutic focus on nonverbal cognition might have positive effects on this important aspect of activity and participation.