The Ottoman Turks
The weakness of the Byzantine Empire after the Fourth Crusade and the collapse of the Mongol Empire during the Black Death of 1347 AD allowed the Ottoman sultans to cross over into Europe in 1352 and begin conquering Greece and the Balkans. By 1361, Murad I had captured Adrianople, and by 1386, Bayezid I had taken Sofia (modern Bulgaria).
Although things were going well in Europe, in West Asia the Mongols regrouped under their new leader Timur and attacked the Ottomans in 1400 AD. The Ottomans lost a lot of their West Asian land to Timur. And they were so distracted by the Mongol attack that their invasion of Hungary also failed. Bayezid was so upset that he killed himself.
Because they were losing their battles in Asia, the Ottomans focused more and more on Europe. They fought many wars with Venice over control of the Eastern Mediterranean shipping routes. In 1453 the Ottoman sultan Mehmed II and his Janissaries even conquered Constantinople (modern Istanbul) from the Byzantine emperors, ending the last piece of the Roman Empire. Mehmed asked for, and got, the leading Venetian painter of his time to come to Constantinople to paint his portrait. Leonardo da Vinci designed what would have been the world's longest bridge for Mehmed's son Bayezid in 1502, though Bayezid was afraid it would collapse and didn't build it.