Christianity split between the Roman Catholic and Orthodox churches in 1054 in the so-called Great Schism.
The two streams separated over the issue of papal supremacy - a key Catholic tenet rejected by the Orthodox - and other dogmatic issues, like the nature of the Trinity and the sacrament of communion.
However, the schism was not the result of a singular great event. Scholars say issues had been building up over time, and in the year 1054 the break became final over a relatively minor issue.
Reconciliation efforts started in the 1960s, following the reforms of Rome's Second Vatican Council, through which the Catholic Church set out to improve relations with other Christians and other faiths.
Pope Paul VI and the Ecumenical Patriarch of Constantinople, Athenagoras - "first among equals" among the Orthodox - met in Jerusalem in 1964 to cancel mutual excommunications issued in 1054.
In 2004, a year before his death, Pope John Paul II returned important relics to both the Constantinople and Moscow patriarchates, in a gesture of outreach to the Orthodox world.
Francis is on good terms with the current Patriarch of Constantinople, Bartholomew, but meeting Kirill marks a turning point in Christian reunification efforts, because he leads the biggest of all Orthodox churches, and the one that was most hostile to Rome.
Francis represents 1.25 billion Catholics, while there are about 225 million Orthodox Christians, two-thirds of them affiliated to the Moscow Patriarchate.
In Cuba, Francis and Kirill are expected find common ground on condemning the persecution of Christians in the Middle East and Africa, but also discuss thorny issues such as the status of the pro-Vatican, anti-Russian Greek Catholic Church in Ukraine.
Healing the 1054 schism remains a far-off prospect.
Experts say the biggest obstacle to it are intra-Orthodox divisions between more than a dozen autonomous churches whose leaders are due to meet for the first time in history June 16-27 in Crete, Greece.