During Carolingian Dynasty, that lasted from 751AD- 987AD, the throne was passed on from father to son. Pepin the Short had three sons and Charlemagne was the one to receive the crown.
Several achievements were acquired by Charlemagne. In 800 he was crowned by the Pope the title of, "Roman Emperor." This was important because the pope claimed the political right to crown the king. During his rule, Charlemagne limited authority of nobles, established royal agents to watch over counts, he opened a palace school and had monasteries to train future monks and priests.
After Charlemagne he crowned his son, Louis the Pious emperor. He wasn't an effective emperor, so his three sons: Lothair, Louis the German, Charles the Bald fought for power. Finally, the Treaty of Verdun was created and it divided the empire into 3 kingdoms and this lead to a weakened central authority and a new governing system called Feudalism.