In the past decades, neuroscientists and clinicians have collected a considerable amount of data and drastically increased our knowledge about the mapping of language in the brain. The emerging picture from the accumulated knowledge is that there are complex and combinatorial relationships between language functions and anatomical brain regions. Understanding the underlying principles of this complex mapping is of paramount importance for the identification of the brain signature of language and Neuro-Clinical signatures that explain language impairments and predict language recovery after stroke. We review recent attempts to addresses this question of language-brain mapping. We introduce the different concepts of mapping (from diffeomorphic one-to-one mapping to many-to-many mapping). We build those different forms of mapping to derive a theoretical framework where the current principles of brain architectures including redundancy, degeneracy, pluri-potentiality and bow-tie network are described.