The filioque was one of the charges laid in the mutual excommunications of 1054 and it remained on the agenda at every attempted reunion afterwards. The councils of Lyons in 1274 and Florence in 1439 both produced formulas of union that the Greek delegations signed and that the Eastern churches at home refused to receive, which tells its own story about where authority in Orthodoxy actually lies.
Modern dialogue has narrowed the theological question considerably by distinguishing two things the word procession can mean. The eternal origin of the Spirit within the divine life is one question; the temporal mission, the sending of the Spirit into the world, is another, and the New Testament plainly describes the Son as sending the Spirit. Much of the Western argument turned out to concern the second. A 1995 clarification issued by the Vatican acknowledged that the Greek term for procession carries a stronger sense of ultimate origination than the Latin equivalent, so that the Latin phrase was never intended to assert what the Greek phrase would have asserted.
Practice has shifted accordingly. Popes have recited the creed in Greek without the addition on ecumenical occasions, and Eastern Catholic churches in communion with Rome generally do not use it. Anglican and some Protestant bodies have recommended dropping it. It remains, however, in the ordinary Latin liturgy, and the procedural objection has not been resolved by any of this: the question of whether a part of the church may amend a common creed is exactly the question of papal authority in another form.
The dispute is a useful case for a comparative reader because it shows how a doctrinal difference that both sides now describe as largely verbal could nonetheless mark a real division, since what was actually at stake was jurisdiction and the two churches' divergent accounts of how the church decides anything.