The Great Napolitan War took place during the years 1425-36.
In 1414, for the first time for centuries, people in Western Europe were horrified again of "Asian hordes": A Seljuk-Barbary fleet crossed the Adria, landed near Taranto / Otranto, swept through Apulia. The king Roberto III of Naples was horrified and asked anyone he could contact for help. Without success: France was still locked in a hard war with England and Castille; the Hungarian king would actually have liked to help, but the powerful nobles forbad him from sending an army south while Hungary proper was threatened; the northern Italian states were busy mopping up the smaller states in the region. The pope called for a crusade, but even that didn't help much. Being desperate, the king made an alliance with Naples' old enemy Aragon, ceding Sicily officially, for once and ever, to them. The new alliance managed to defeat the Seljuks in the South. Especially their cannons helped them a lot to reconquer the cities. Only Taranto and Bari in Apulia were held by the Seljuks. In 1418, an armistice was made - but both sides planned to restart war, when the time would be right.
After the Seljuks had managed to hire an expatriate Italian willing to equip their army with cannons, they restarted the war. Initially successful, the situation changed when in 1427 France entered the war on Anjou Naples' side, even cancelling the second Aquitainian War to do so.
After the French almost had managed to defeat the Rum-Seljuks, the latter were exceptionally lucky in 1431: During the battle, king Charles IV was captured. He had to promise to leave the war to be released again. Now the tides of war turned again.
In 1436, after king Roberto had fallen in battle, the greater part of Naples became a part of the Seljuk empire. Only the western third with Pescara, Benevent, and Naples itself survived as a tributary.