Just as other parts of speech, the concept of the adverb is a hybrid concept, combining structural and semantic criteria.

The structural criterion is insufficient by itself because in most languages, words of other classes may function as adjuncts, too. It was traditionally sharpened by the additional requirement that the words in question do not inflect. If this is to work at all, it must be provided by some reserves:

.pueraccurritvelox
Latinboy(NOM.SG)come.running:3.SGfast:NOM.SG
the boy comes running fast

Some of these reserves need refinement in order not to be ad hoc.

The functional criterion characterizes a class that is semantically rather heterogeneous. As a consequence, those words differ somewhat in their distribution, and it becomes hard to determine a common denominator.

Thus, both the structural and the functional approach are insufficient by themselves. They must be combined so that they converge on a set of words.

Apart from this semantic heterogeneity, the class of adverbs is heterogeneous just like the other major classes (noun, adjective, verb) because it includes lexical elements like downwards and grammatical elements like there. Therefore, the distribution of lexical and of grammatical adverbs must be determined independently.