They were considered by the Romans as Phoenicians, the word Punic means Phoenician. In the Aeneid, the "history" of Carthage is explained as a journey away from Tyre, queen Dido's home city. One of the only copies of Carthaginian writing comes from Mago, who wrote on Carthaginian agriculture. It was translated into Greek and Latin. Pliny the Elder tells us of these translations, one commissioned by the Senate. I don't think enough information exists from after the razing of Carthage by Scipio Aemilianus. The Romans held a deep resentment for them and as they became masters of the Mediterranean, Carthaginian culture was basically erased.

Sources: Pliny the Elder, Plutarch, Appian, Columella