Since the Enlightenment period, natural theories of speech and language evolution have florished in the language sciences. Four ever returning core issues are highlighted in this paper: Firstly, Is language natural to man or just an invention? Secondly, Is language a specific human ability (a ‘language instinct’) or does it arise from general cognitive capacities we share with other animals? Thirdly, Has the evolution of language been a gradual process or did it rather suddenly arise, due to some ‘evolutionary twist’? Lastly, Is the child's language acquisition an appropriate model for language evolution?