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The Church invested kings with powers, and on occasion deposed them. In early Middle Ages the relationship of power was such that the kings had something akin of domestic church, which advised them but derived its power through the king's political power. It changed in the aftermath of the so-called investiture controversy in eleventh century (Conflict of Investitures).

The striking example of the new power of papacy was when Henry IV was standing on his knees in the snow at Canossa asking Pope Gregory VII (not Gregory II as I posted from memory previously) to absolve his sin and restore his power.

At a meeting of the German lords, spiritual and temporal, held at Tibur in October, 1076, the election of a new emperor was canvassed. Onlearning through the papal legate of Gregory's desire that the crown should be reserved for Henry if possible, the assembly contented itself with calling upon the emperor to abstain for the time being from all administration of public affairs and avoid the company of those who had been excommunicated, but declared his crown forfeited if he were not reconciled with the pope within a year. It was further agreed to invite Gregory to a council at Augsburg in the following February, at which Henry was summoned to present himself. Abandoned by his own partisans and fearing for his throne, Henry fled secretly with his wife and child and a single servant to Gregory to tender his submission. He crossed the Alps in the depth of one of the severest winters on record. On reaching Italy, the Italians flocked around him promising aid and assistance in his quarrel with the pope, but Henry spurned their offers. Gregory was already on his way to Augsburg, and , fearing treachery, retired to the castle of Canossa. Thither Henry followed him, but the pontiff, mindful of his former faithlessness, treated him with extreme severity. Stript of his royal robes, and clad as a penitent, Henry had to come barefooted mid ice and snow, and crave for admission to the presence of the pope. All day he remained at the door of the citadel, fasting and exposed to the inclemency of the wintry weather, but was refused admission. A second and a third day he thus humiliated and disciplined himself, and finally on 28 January, 1077, he was received by the pontiff and absolved from censure, but only on condition that he would appear at the proposed council and submit himself to its decision.
Henry then returned to Germany, but his severe lesson failed to effect any radical improvement in his conduct. [...]
(Pope St. Gregory VII)

Since then, unevenly and gradually, the Church asserted its supremacy over political powers of the day. The modern doctrine of subsidiarity, where local political power has autonomy in local matters while the Church has ultimate authority in fundamental universal matters is a corollary of this kingship of Christ. It was, by the way, well understood by American Founding Fathers whose slogan was "no king but Christ".