Kaykaus I in the context of "Siege of Sinope"

Alexios I Megas Komnenos (Greek: Αλέξιος Κομνηνός; Georgian: ალექსი კომნენოსი; c. 1182 – 1 February 1222) or Alexius I Megas Comnenus with his brother David, the founder of the Empire of Trebizond and its ruler from 1204 until his death in 1222. The two brothers were the only male descendants of the Byzantine Emperor Andronikos I, who had been dethroned and killed in 1185, and thus claimed to represent the legitimate government of the Empire following the conquest of Constantinople by the Fourth Crusade in 1204. Although his rivals governing the Nicaean Empire succeeded in becoming the de facto successors, and rendered his dynastic claims to the imperial throne moot, Alexios' descendants continued to emphasize both their heritage and connection to the Komnenian dynasty by later referring to themselves as Megas Komnenos ("grand Komnenos").

While his brother David conquered a number of Byzantine provinces in northwestern Anatolia, Alexios defended his capital Trebizond from an unsuccessful siege by the Seljuk Turks around the year 1205. Further details of his reign are sparse. Muslim chroniclers record how, in 1214, Alexios was captured by the Turks in the field while defending Sinope; despite sending an envoy to seek their surrender the city refused to capitulate to Sultan Kaykaus I, and Alexios was tortured in sight of the Sinopians. The city submitted to Kaykaus and Alexios was freed after becoming Kaykaus' vassal. Alexios died at the age of forty.

The Trapezuntine emperors were the rulers of the Empire of Trebizond, one of the successor states of the Byzantine Empire founded after the Fourth Crusade in 1204, until its fall to the Ottoman Empire in 1461. All but two of the Trapezuntine rulers belonged to the Komnenos dynasty, which had previously ruled the Byzantine Empire from 1081 to 1185. They initially claimed to represent the legitimate line of Roman emperors, in opposition to the Latin Empire in Constantinople, the Laskaris dynasty of the Nicene Empire, and the Komnenos Doukas family of Epirus and Thessalonica. To emphasize their dynastic claim, Trapezuntine emperors from the late 13th century onwards styled themselves as Megas Komnenos (Μέγας Κομνηνός, lit. 'Grand Komnenos').

Out of the Byzantine claimants that emerged in 1204 and thereafter, the Trapezuntine emperors, despite their illustrious descent, had perhaps the worst position. Not only were they far away from Constantinople in a peripheral province of the empire, but the reputation of the Komnenoi had been severely damaged by the detested last emperor of the dynasty, Andronikos I Komnenos (r. 1183–1185), grandfather of the first Trapezuntine emperor Alexios I (r. 1204–1222). Though they continued to claim to be the legitimate rulers of the entire former Byzantine Empire for decades thereafter, conflict with the Nicene Empire and the Sultanate of Rum in the early 13th century reduced the power of the Trapezuntine emperors. After the fall of Sinope to Sultan Kaykaus I in 1214, the Empire of Trebizond ceased to be a major contender for restoring the Byzantine Empire and became reduced to a small and local power.

The following is a list of the Seljuk Sultans of Rum, from 1077 to 1307. The sultans of the Seljuk Sultanate of Rûm were descended from Arslan Isra'il, son of the warlord Seljuk. The Seljuk Empire was founded by Chaghri and Tughril, sons of Arslan's brother Mikail ibn Seljuk.

• Suleiman I, son of Qutalmish, 1077–1086
• Abu'l Qasim (self-declared, Nicaea), appointed by Suleiman ibn Qutulmish, 1084 (Not a member of House of Seljuk)
• Kilij Arslan I, son of Suleiman ibn Kutalmish, 1092–1109
• Malik Shah, son of Kilij Arslan, 1109–1116
• Mesud I, son of Kilij Arslan, 1116–1156
• Kilij Arslan II, son of Mesud I, 1156–1192
• Kaykhusraw I, son of Kilij Arslan II, 1192–1197
• Suleiman II, son of Kilij Arslan II, 1197–1204
• Kilij Arslan III, son of Suleiman II, 1204–1205
• Kaykhusraw I (second rule), 1205–1211
• Kaykaus I, son of Kaykhusraw I, 1211–1220
• Kayqubad I, son of Kaykhusraw I, 1220–1237
• Kaykhusraw II, son of Kayqubad I, 1237–1246
• Kaykaus II, son of Kaykhusraw II (sole rule) 1246–1248
• Kaykaus II (joint rule), 1248–1259 (with Kilij Arslan IV, 1248–1259, with Kayqubad II, 1249–1257)
• Kilij Arslan IV, son of Kaykhusraw II (joint rule), 1248–1259 (with Kaykaus II, 1248–1259, with Kayqubad II, 1249–1257)
• Kayqubad II, son of Kaykhusraw II (joint rule), 1249–1257 (with Kaykaus II and Kilij Arslan IV)
• Kilij Arslan IV (sole rule), 1259–1265
• Kaykhusraw III, son of Kilij Arslan IV, 1265–1282
• Mesud II, son of Kaykaus II, 1282–1284
• Kayqubad III, son of Faramurz (son of Kaykaus II), 1284
• Mesud II (second rule), 1284–1293
• Kayqubad III (second rule), 1293–1294
• Mesud II (third rule), 1294–1301
• Kayqubad III (third rule), 1301–1303
• Mesud II (fourth rule), 1303–1307
• Mesud III (1307-1308)
• Kilij Arslan V ( Claimant Sultan 1308-1318)

The Seljuk Sultanate of Rum dissolved into many Anatolian Beyliks, one of them being the future Ottoman Empire in 1307.