Celtiberians spoke a language inherited from Continental Celtic, related to Gaulish and Lepontic. But the main distinguishing feature is that Celtiberians acquired much of phonetics and lexics from non-Indo-European Iberian languages; that is reflected in placenames and names of deities. Nevertheless we can state for sure that the language belonged to Q-Celtic, so Indo-European kw- grew into q here. In fact the structure of Celtiberian grammar remained completely Celtic. The nouns are inflected, having sometimes a sibilant -s' instead of Indo-European -s. The language used about five or six cases (with accusative, dative, instrumental); the dative plural had the Italo-Celtic -b- suffix after the stem. The plural nominative either preserves Indo-European -es or develops a European -i. There is also one strange ending for genitive singular: -o which cannot be seen anywhere else in the Indo-European family.
Only two verbs are known from Celtiberian, but they witness clearly that verb endings remained Indo-European, with -t in the 3rd person singular and -nti (a primary ending) in the 3rd person plural.
Celtiberians were easily assimilated by Romans in the last centuries BC, and their language, the product of mixture of different language families, disappeared.