In the infamous 4th crusade, the republic of Genoa managed to acquire some islands in the Aegean Sea. In 1253, the republic acquired Safi in Morocco. Thanks to a trade with Nikaia in 1265, they took over the Aegean islands of Lesbos, Chios and Samos, which Nikaia couldn't defend alone against the Rum-Seljuks. 1284, they defeated Pisa, acquired Elba, Sardinia and Corsica. In 1306, the republic sold Rhodos to the Order of the Johannites. After Constantinople fell in 1327, many Byzantines fled to Genoa too, helping to spawn the Rinascita. OTOH, the republic lost economical and political power by this development too, since they had lost the trade with the Byzantine Empire and the Black Sea countries. 1336, they had to fight a short war against France under the young king Jean I. In 1366, it was defeated by its old rival Venice, which wasn't too much better off itself, though - in the 2nd half of the 14th century, beggar hordes created by repeated famines made life hard for all the states of northern Italy. 1399, they had to sell Corsica to Florence, which planned to build up a fleet too. 1402, a combined strike of the Rum-Seljuks and the Barbary pirates of North Africa went against Genoa, which lost its islands in the Aegean Sea.
The end came in 1407, when Florentine diplomat Maffeo Servitore came up with his plan to divide all of Northern Italy between Savoy, Venice and Florence. Although this plan didn't include Genoa, it was invaded and subsequently annexed by Savoy in the war from 1430-35. The Savoyan duke treated the conquered city relatively well, though; he wanted to use it to become a power in the Mediterranean, too.
Genoa under Savoyan and Italian rule