The Phoenicians mainly interacted with the world through trade and the act of fighting nearly every group of people they interacted with. But here is how they interacted with various peoples.
The Mediterranean
The Mediterranean was the primary "hunting grounds" of the Phoenicians, as they did most of their trade here, and most of their conquering as well. The spread of the Phoenician alphabet through the Mediterranean was due to their trade and conquering as well, and the areas around Phoenicia's main cities benefitted from their rich literature, though unfortunately not much of their books and knowledge has survived the centuries. The Phoenicians monopolized most of the Mediterranean trade throughout various outposts and cities to control the area and prevent their rivals from getting through.
The Americas
The possibility that the Phoenicians may have made a pre-Columbian voyage or voyages to the Americas has been explored by several people from as early as T. C Johnston's 1892 book, "Did the Phoenicians Discover America?". Work on Phoenician coins carried out by Mark McMenamin suggests that gold coins minted in Carthage between 350 and 320 B.C.E. may depict a map of the Americas. Some sources have speculated that the Phoenicians may even have colonized the Americas. Thor Heyerdahl's Ra I and Ra I expeditions were designed to prove that Egyptian ships could have crossed the Atlantic but could also be applied to the Phoenicians, who were renowned for their seamanship and who were often employed as sailors and explorers by the Egyptians. Some first century peruvian pottery resembles Phoenician pottery. Wreckage of Phoenician ships and an inscription on a rock in Brazil suggests Phoenicians had visited there. While it is widely agreed upon by experts on Middle Eastern and African history that African peoples used their far more advanced sailing ships to travel to the Americas before Europeans, the Phoenician theory still has some speculation about it.