Human language is both highly diverse-different languages have different ways of achieving the same functional goals-and easily learnable. Any language allows its users to express virtually any thought they can conceptualize. These traits render human language unique in the biological world. Understanding the biological basis of language is thus both extremely challenging and fundamentally interesting. I review the literature on linguistic diversity and language universals, suggesting that an adequate notion of 'formal universals' provides a promising way to understand the facts of language acquisition, offering order in the face of the diversity of human languages. Formal universals are cross-linguistic generalizations, often of an abstract or implicational nature. They derive from cognitive capacities to perceive and process particular types of structures and biological constraints upon integration of the multiple systems involved in language. Such formal universals can be understood on the model of a general solution to a set of differential equations; each language is one particular solution. An explicit formal conception of human language that embraces both considerable diversity and underlying biological unity is possible, and fully compatible with modern evolutionary theory.