Communication is a highly complex human task depending on a neurologically widespread and simultaneous interplay between a range of sensory, motor, and cognitive functions. This makes the neurobiological basis of communication sensitive and vulnerable to brain injuries, and therefore communication disorders after a brain injury are common. After a short introduction to brain areas involved in the intact function of speech, language, and communication, three frequent and distinct communicative disorders are presented: dysarthria affecting motor speech production, aphasia affecting language at the linguistic levels of phonology, semantics, and grammar, and cognitive-communication disorders affecting adequate communication in social interaction. Definitions, anatomical localization, and clinical symptoms of each of these disorders as well as the distinctive features across them are described. Furthermore, specific interventions based on principles of neuroplasticity are highlighted. These include therapies that harness the brain’s capacity to reorganize and adapt, thereby improving communication abilities in individuals with communication disorders. The insights provided are crucial for clinicians providing neurorehabilitation for people with communication disorders following brain injury.