filioque clause into the Nicene Creed; the use by the Western church of unleavened bread for the Eucharist; disputes in the Balkans over whether the Western or Eastern church had jurisdiction; and disputes over whether the Patriarch of Rome (the Pope) should be considered a higher authority than the other Patriarchs. This lead to the exchange of excommunications by the representative of Pope Leo IX and the Patriarch of Constantinople Michael Cerularius in 1054 (finally abolished in 1965) and the separation of the Roman Catholic and the Orthodox churches. Though there have been frequent attempts to settle differences the breach has not been healed, except for a brief moment before the fall of Constantinople to the Turkish army.
Papacy from Avignon to Rome by Pope Gregory XI in 1378, ending the Avignon Papacy.
After Gregory XI died, the Romans rioted to ensure an Italian was elected; the cardinals, fearing the crowds, elected an Italian, Pope Urban VI in 1378; but in the same year the majority of them removed themselves to Fondi, and elected a rival Pope from there, Pope Clement VII. Later a council at Pisa was held in 1409 to try to solve the dispute, but it only resulted in the election of a third Pope, Pope Alexander V by the council, soon to be followed by Pope John XXIII.
Finally, the Council of Constance in 1417 deposed John XXIII and the Avignon Pope Benedict XIII, received the resignation of the Roman Pope Gregory XII, and elected Pope Martin V, thereby ending the schism.
From this time forward in the Catholic church it was decreed explicitly that no Council had power over the Popes, and there is no way to undo a Papal election by anyone but the pope.
The alternate papal claimants have become known in history as antipopes.