Pope Clement V, who approved the order to arrest all the Templars, had earlier told them to merge with the Hospitallers, since it didn't seem necessary to him to have two groups who were performing the same function: guarding/assisting people traveling to the Holy Land. Who were the Hospitallers?
In 1023, a hospital was built in Jerusalem on the site of the Benedictine monastery of St. John the Baptist, to care for sick and injured pilgrims. When Jerusalem was taken over by the First Crusade, some Crusaders formed the Order of Saint John of Jerusalem—colloquially known as the Hospitallers—to support the hospital. A papal charter charged them with the care and defense of folk in the Holy Land. This evolved from caring for people to providing military escorts and then to fighting in wars for Christendom.
Once Jerusalem was retaken by Muslims, the Hospitallers made their home base in Rhodes. Even later they had to relocate to Malta. They spread far and wide, establishing a presence in England and Normandy by 1200. They spread to Ireland, to Hungary, to Russia, and of course around the Mediterranean. They even made a presence in North America: they briefly colonized four Caribbean Islands—including Saint Martin and Saint Barts—which they gave to France in the 1660s.
The Knights had a bad time during the Protestant Reformation of the 1500s when several large Northern European sections of the order broke from their Roman Catholic roots. The French Revolution abolished the Order in France along with abolishing feudalism and tithes.
The Sovereign Military Hospitaller Order of Saint John of Jerusalem, of Rhodes and of Malta, more commonly known now as the Sovereign Military Order of Malta, is considered the successor to the Hospitallers. The Order headquartered in Rome as of 1834; they performed extensive hospital work during the two World Wars.
About that original hospital: it was excavated between 2000 and 2013, and was a replacement for an even earlier hospital. I'll talk about that next time.