Emperor
The first Austrian Emperor was the last Holy Roman Emperor Francis II. In the face of aggressions by Napoleon, Francis feared for the future of the Holy Roman Empire. He wished to maintain his and his family's Imperial status in the event that the Holy Roman Empire should be dissolved, as it indeed was in 1806 when an Austrian-led army suffered a humiliating defeat at the Battle of Austerlitz. After which, the victorious Napoleon proceeded to dismantle the old "Reich" by severing a good portion from the empire and turning it into a separate Confederation of the Rhine. With the size of his imperial realm significantly reduced, Francis II, "Holy Roman Emperor" became Francis I, "Emperor of Austria". The new imperial title may have sounded less prestigious than the old one, but Francis' dynasty continued to rule from Austria and a Habsburg monarch was still an emperor ("Kaiser"), and not just merely a king ("König"), in name.
Roman Empire
Several states claimed to be the Roman Empire's successors after the fall of the Western Roman Empire. The Holy Roman Empire, an attempt to resurrect the Empire in the West, was established in 800 when Pope Leo III crowned Frankish King Charlemagne as Roman Emperor on Christmas Day, though the empire and the imperial office did not become formalized for some decades. After the fall of Constantinople, the Russian Tsardom, as inheritor of the Byzantine Empire's Orthodox Christian tradition, counted itself the Third Rome (Constantinople having been the second). These concepts are known as Translatio imperii.