Carthage was founded about 800 BCE (maybe slightly later, probably not earlier) by Phoencians from the metropoleis of Sidon and Tyre, and our current understanding is that the city was already very large and important by 700 BCE. That is--it was dominate from its very founding. The foundation myth talks about a refugee Queen (Dido or Elissa or Elishaya) fleeing political oppression in her home city. That is almost certainly a later re-interpretation of a much more complicated process.

The Phoenicians had been sailing into the western Med. since the 10th or 9th century, almost certainly in search of metals. We find them creating small enclaves (trading posts or emporia) along North Africa, in Sicily, on Sardinia, and along the southern coast of Spain. They even went out into the Atlantic and around the northwestern coast of Africa. Everything about the archaeology of these places suggests that they were extractive in nature: the goal was to pull precious metal raw materials out of the West and return them to the Levant to be processed into luxury items like jewelry and furniture fittings. The site of Carthage probably began as a sort of headquarters in the west for this venture, and the archaeology shows lines of flow between Carthage and several important western sites, like Gadir (Cadiz), the Andalulsian emporia, Sardinia, western Italy (Etruscans), and Sicily. We also find some evidence of goods production in Carthage itself. In the 8th century, however, the assumption is that Carthage was a stop-over or clearinghouse for traffic flowing west to east.

During the 7th and 6th centuries, Carthage continually grows larger. Part of this could be the success of the city in its position between east and west, and part is probably due to increasing tendency for Phoenicians from the mother cities to sail west and never return to the Levant. In these centuries, the Assyrians and the Egyptians (as they continually battled) were putting a lot of pressure on the Phoenician mother cities. It is very difficult to say for sure, but I suspect that there was a general movement out goods and people out of the Levant and into the western Med.

At this point, Carthage begins to slowly cut ties with the the Near East and to become the homeland herself a new, western Phoenician presence. At this point archaeologists normally drop the "Phoenician" moniker and begin calling the material culture "Punic." To keep it simple: in the archaeology, we see less and less "eastern" material and we see clear signs of the reinforcement and expansion of "western" routes, the heart of which was Carthage. Major Punic cities now ply the western waters routinely, with centers at Motya (western Sicily), several urban centers on Sardinia, Gadir (Cadiz) in Spain, and a few smaller enclaves to the west of Carthage along the North African coast (at later Utica, for instance).

Culturally, Carthage remains "Phoenician" but with some interesting shifts. In religion, the old Phoenician gods remain, with Baal and Astarte and Eschmoun all receiving attention. But deities which had played an apparently lesser role in the mother cities of the Levant now come to the fore. Melquart seems to enjoy a rise in popularity (he was a sort of Herakles with nautical elements, a bit of a cross between Herakles and Poseidon and a pirate).

And, importantly, Tanit comes to the fore. She was the consort of Baal and was associated with the sea. In Carthage, at a place near the Great Harbours called the Tophet, modern excavators have confirmed the practice of child sacrifice to Baal and Tanit. It is suspected that the practice originates in the east, in the Phoenician culture, but has never been satisfactorily confirmed there by archaeology. In the west, the presence of a tophet (burial ground specifically for sacrificed children) becomes one of the major markers for urban development. We have tophets or their telling remnants in several large Punic sites in the western Med in the period 8th-5th centuries BCE.

Carthaginian culture also shifted slightly away from the focus on the sea, though the city remained the master of western Mediterranean waters until the Punic Wars and control of trade remained her primary objective. Still, unlike the mother cities of the Levant, the hinterland of Carthage was vast and fertile and relatively unoccupied. Through a series of negotiations and conflicts, Carthage steadily expanded her agricultural lands in Tunisia. We find evidence of extensive Punic irrigation works and large towns, including the famous circular town of Kerkouanne on Cap Bon.

For much more on Carthage, see S. Lancel Carthage (either in the orig French or translated), 1995. The book is a bit dated now as far as the latest archaeological work, but it is still good for an overview.