Short answers, pulled from the story.
The Empire of Trebizond was a Byzantine successor state that occupied a narrow strip of the southeastern Black Sea coast from 1204 to 1461. It was ruled by the Grand Komnenoi, a dynasty descended from the deposed Byzantine emperor Andronikos I Komnenos. Among the three Byzantine successor states that emerged after the Fourth Crusade, Trebizond survived the longest.
The empire was founded in April 1204 when Alexios Komnenos and his brother David seized Trebizond with troops from Queen Tamar of Georgia. Alexios was twenty-two years old at his proclamation as emperor. Both brothers were grandsons of Andronikos I Komnenos, the last Komnenian Byzantine emperor.
Trebizond's wealth rested on its position at the southeastern terminus of the Silk Road. After Hulagu Khan destroyed Baghdad in 1258, trade shifted north through the Black Sea, making Trebizond the main gateway between Asia and European markets. The empire also exported Pontic silver, alum, wine, and hazelnuts.
The princesses of Trebizond were famous for their beauty and generous dowries, a reputation noted by historians Steven Runciman and Donald Nicol. Marriage alliances were a key diplomatic tool of the empire. Alexios IV gave daughters to two Turkish khans; his eldest daughter Maria married the Byzantine Emperor John VIII Palaiologos.
The Empire of Trebizond fell on the 15th of August 1461, when Emperor David surrendered to Ottoman sultan Mehmed II after a month-long siege. Mehmed had first captured Sinope and neutralized the empire's chief ally before attacking Trebizond. David and his family were taken into captivity.
The Principality of Theodoro in Crimea was an offshoot of the Empire of Trebizond. It survived the fall of Trebizond by fourteen years, finally falling to Ottoman forces on the 30th of December 1475.