Grammatical Functions

 The article The Functions of Adverbs and Adverb Phrases in English, explains the six grammatical functions of adverbs and adverb phrases in English grammar: adverb phrase head, adjective phrase modifier, adverb phrase modifier, verb phrase modifier, adverbial, and adjunct.

The article English Adverbs and Adverb Phrases: The Five Main Functions of Adverbs in the English Language identifies and exemplifies five grammatical functions of adverbs and adverb phrases in English grammar.

Adverb Clauses

As described in the article The Forms and Functions of Clauses in English: Verb Clauses, Noun Clauses, Adjective Clauses, and Adverb Clauses, the grammatical function of the adverb clause in English grammar is adverbial.