This review focuses on language deficits in post-stroke aphasia, their rehabilitation and potential new developments based on current knowledge of human brain function. Language impairments in post-stroke aphasia often become chronic and cause significant communicative difficulties for patients. Though standard rehabilitation methods provide some language improvements, they are usually moderate and often decay over a period of time. These traditional rehabilitation approaches are usually based on existing conventions formed through decades of clinical practice; whilst valuable, they are not often rooted in up-to-date neuroscientific knowledge. In recent decades, human neuroscience has developed at a very high speed, not least due to the advent of non-invasive brain imaging techniques. Currently, it has reached the stage where neuroscientific knowledge can inform clinical practice, and help upgrade the traditional approaches using modern neuroscience tools. Furthermore, traditional practices typically apply the same routines to different patients, even though the nature of the individual deficit – and hence the care needed – are never the same. For instance, aphasic patients demonstrate a massive variety of improvement patterns during natural language recovery. This might be caused by individual differences in the functioning of language neural networks and their dynamics after stroke. Although the problem of individual variability in aphasia is well-known, there is still no comprehensive understanding of all factors that impact this variability. As we highlight in this review, the issue is of high importance for planning language therapy on individual basis. We also analyze neuroscientific underpinnings and clinical efficiency of a language therapy, which is widely used for chronic aphasia rehabilitation – constraint-induced aphasia therapy.