Contradictions in interpreting data from different scientific domains exploring anthopogenesis and language evolution will remain unsolved without a convergent approach and mutually acceptable multidisciplinary language. The article addresses the question of specific features of mental functions and language in humans as compared to other species. The main hypotheses of human evolution and their language are discussed. Cognitive capacities of animals and their communication signals are addressed, as are the basic principles of brain functions and bio-evolutionary mechanisms that underlie the complexity of human behavior and language evolution. Human language is a species’ specific brain ability, promoting not only complex communication signals, but also mentality itself. Language has basic universal rules, possibly caused by brain networks per se. It is hierarchically organized within the levels of lexicon, grammar (morphology, syntax, semantics and phonology) and pragmatics. The functions and their brain mechanisms are currently discussed either within the localizationistic modular approach, or within holistic views. The main discussions are between scholars exploring universal inborn grammar, and those preferring connectionism based on neuronal net learning, frequency factors, etc. One of the features of language in contrast to other communication systems is its principal ambiguity on many linguistic levels, context being a crucial aspect.