Mongol Invasion of the Crimea
The Mongols lead by Guyuk Khan invaded the Byzantine province of Crimea in 1241, as part of their plan to invade Europe and expand the Mongol Empire across the world. But the Byzantines in the Crimea proved a challenge as the Mongols were originally defeated in their attempt to capture Kerch, and were then forced on to the Crimean by land up north. The city of Simferopol fell in May 1241, and eventually Yalta, the Byzantines retreated from the peninsula finally in June, but destroyed all the ports, leaving the Mongols stranded on the Crimea.
The Mongols brought in hundreds of ships to cross the Black Sea and did so in August 1241, where they then landed on the eastern Anatolian peninsula after a Byzantine naval blockade forced them away from the main length of the Anatolian.
Mongol Invasion of Anatolia
The Mongols landed at Trabzon in August 1241, where they then proceeded to capture the city, and moved west to capture the rest of the Byzantine Anatolia. Samsun fell to a short Mongol siege in November 1241, and then a lengthy campaign to capture Ankara ensued. The campaign lasted 5 months, and ended in a Mongol defeat at Ankara, where 8,000 Mongols were killed, and eventually forced back to Samsun, where they remained until April 1242.
The Byzantines launched a counterattack in May 1242, where they then pushed the Mongols off the Anatolian, recapture Trabzon, and then moved to defeat them ultimately at the Battle of Kars. The Mongols retreated back up to the Crimea, where they were then faced with a Byzantine rebellion in Yalta, which they then crushed and were able to bring in reinforcement. Guyuk Khan then forced his tired troops into a short campaign around the Black Sea on the Balkan peninsula, for the final campaign of the war.
Mongol Invasion of the Balkans
The city of Varna fell to the Mongols in February 1243, where they then moved on a campaign for Constantinople, which they first laid siege to in late March 1243. After the siege was lifted two weeks later, the Mongols went campaigning Greece, capturing Thessaloniki in May, and then laying siege to Athens in June, but their siege was repulsed after a short break-out battle was fought, and they were then pursued by a mounting Byzantine army, which recaptured Thessaloniki in July, and then forced them into a small pocket of resistance centered around Adrianople by late July.
The Byzantine army had grown to 140,000 against the remaining Mongol army of 80,000, who then brokeout, at the loss of 5,000 troops, and laid a second siege against Constantinople. They were eventually defeated after 3 weeks, and forced into another small pocket, which surrendered to the Byzantines in December 1243, but found that the Mongol Khan, Guyuk Khan had been killed after the Second Siege of Constantinople had been lifted. Among the units surrendered were two early model Mongol cannons, which were then sent to be studied by Byzantine scientist, who also learned the recipe for gunpowder, giving rise to the use of gunpowder in the Byzantine Army.