In my amateur history reading I always seem to hear about the Carthaginians through Roman and Greek accounts. Are there no first-hand accounts? For a people so rich and powerful throughout both the Greek and Roman periods (well, until Rome destroyed them), and whose wider Phoenician ancestry contributed to the adoption of writing (not to mention the alphabet) in Greece, is there not something strange about this silence?
Did they not keep records of trade and other activities? Did they not have political discussion? Did they use particularly non-durable writing materials? Or were their writings all destroyed by Rome? Or destroyed later maybe, by Islam? Were no non-Roman histories of the region written in the centuries after the fall of Carthage?
Hello there! Unfortunately, almost nothing has survived of Phoenician-Punic literature. All that remains of historical records, for instance, are some Greek translations of Tyrian histories (which we only have secondhand through Josephus) and a reference to the capture of Agrigentum in 406 BC found in a Punic inscription. One might also include the Greek translation and abridgment of Hanno's Periplus, which describes a Carthaginian naval expedition beyond the Straits of Gibraltar. The loss of all their other writings seems to be a product of time rather than deliberate destruction. The Carthaginians, at least, kept some records on papyri--archaeologists have found numerous clay seals that would have sealed papyri rolls--but these are extremely perishable. We also know that the Romans spared the state library of Carthage when they destroyed the city and subsequently gave its contents to the Numidian kings, who spoke and read Punic; the Punic language, moreover, saw continued use throughout North Africa several centuries afterwards. Punic books were apparently still around in the time of Saint Augustine, as he himself claims. What ultimately happened to them is unknown.
That said, we do possess about ten thousand inscriptions (more turn up each year) from throughout the Mediterranean written in Phoenician, Punic, or Neo-Punic. The majority of these are brief and probably quite boring to the average reader: ex-votos ("for the gods, a vow which Bob vowed"), names ("[amphora] belonging to Bob son of Jim"), funerary inscriptions ("Bob built this gravestone for his father Jim"), etc. There are more interesting ones as well, such as the royal inscriptions of the kings of Sidon, Tyre, Byblos, and Kition and Idalion, or religious and economic texts from Carthage and its vicinity. All of these continue to receive attention from Biblical and Near Eastern scholars but have largely been ignored (or, more recently, misinterpreted) by historians specializing in Greece and Rome. Of course, there is no easy way to access these inscriptions--let alone find up-to-date translations--which can make research difficult for non-specialists (though I am trying to fix that; I've translated and partly annotated about fifty texts so far). One can still hope for more collaboration between the disciplines in the future!