A generative grammar is made up of a set of rules that make it clear which sequences of words and phrases are possible. Noam Chomsky first put forward the idea of a generative grammar. Chomsky himself formulated three models, the finite-state, phrase-structure and transformational. Since then other linguists have added other models. The rules of the grammar are explicit, allocating a structural description to each phrase. A generative grammar would allow someone to generate an unlimited number of new phrases in a language, provided the known necessary vocabulary.

A descriptive grammar is made up of a set of collected utterances made by native speakers of a particular language. The creation of descriptive grammars was popular amongst American linguists at the turn of the last century who were attempting to record the dying languages of the Native American Indians. Linguists analyze the language by studying the patterns of phonology as well as the syntax of the utterances. There is little interest in the actual meaning of the phrases. The overall aim of a descriptive linguist is the formulation of discovery procedures that would enable the systematic description of any language. The reader of a descriptive grammar would be able to determine what is or is not a proper sentence grammatically, even if he or she does not understand the sentence.

Prescriptive grammars are produced by language purists in order to instruct the reader in how the particular language 'should' be spoken. Rather than describing the rules, a prescriptive grammar prescribes them. As such if the rules of a language were to change new generative and descriptive grammars would be necessary while a prescriptive grammar might attempt to reverse the change, or pollution of the language. In addition, prescriptive grammars work to prevent change.

Pedagogic grammars are teaching grammars. They are for reference or work. They can be comprehensive, but more often than not they are more modest. Unlike a prescriptive grammar that states what the rule of language are or should be, a pedagogic grammar merely draws attention to the rules. In this way a pedagogic grammar is a combination of a prescriptive and descriptive grammar. They are designed to aid foreigners in learning a language or help native speakers (such as undergraduate students reading linguistics at Oxford) understand their own language. They are for teachers and students alike.