The detail
In 858 Patriarch Ignatius of Constantinople was forced out amid court politics, and Photius, a lay scholar and imperial official, was rapidly ordained and installed. Ignatius's supporters appealed to Rome. Pope Nicholas I, after his legates had accepted Photius at a synod in Constantinople (861), repudiated them, and a Roman synod in 863 declared Photius deposed and Ignatius the lawful patriarch. At stake was not only one appointment but whether the pope could judge the internal affairs of the see of Constantinople.
The dispute widened over Bulgaria. Khan Boris I was baptised by Byzantine clergy (c. 864) but then turned to Rome, and Latin missionaries arrived. In 867 Photius sent an encyclical to the Eastern patriarchs attacking Latin practices in Bulgaria and, above all, the addition of the Filioque ("and the Son") to the Creed, which he treated as a doctrinal error and not merely an irregular insertion. A synod in Constantinople that year declared Nicholas deposed. Later Photius developed his argument for the procession of the Spirit "from the Father alone" in the Mystagogy of the Holy Spirit.
Politics then reversed the situation. In 867 Basil I seized the throne, removed Photius and restored Ignatius. A council held in Constantinople in 869–870 with papal legates condemned Photius. Ignatius died in 877, Photius returned as patriarch, and with the agreement of Pope John VIII a large council in Constantinople (879–880) recognised him, annulled the acts of 869–870, and reaffirmed the Creed without additions. Bulgaria eventually remained in the Byzantine ecclesiastical sphere.
Historians now generally read the episode as a reconciliation rather than a lasting break. Francis Dvornik's influential research (1948) argued that there was no "second Photian schism" and that Photius died in communion with Rome. But the two councils are remembered differently. From the late 11th century, Western canonists, partly because its canons opposed lay interference in episcopal elections, counted the council of 869–870 as the Eighth Ecumenical Council, as the Catholic Church still does. Many Orthodox regard 879–880 as authoritative and some call it the Eighth Ecumenical Council; Photius is venerated as a saint in the Orthodox Church.
How each side tells it: older Latin accounts present Photius as an ambitious usurper who rebelled against legitimate papal authority and began the schism; Orthodox accounts present him as a defender of the Creed of Nicaea and of the equality of patriarchates against Roman overreach. Modern historians on both sides tend to emphasise the mix of court factions, rivalry over Bulgaria and genuine theological difference, and the fact that full communion was restored in 879–880.