Bishops have always been appointed. When Christianity was first developing, that process was more localized, and the bishops might have to ability to steer the choice of their successor. By the time of the early middle ages, bishops were supposed to be appointed by the pope. However, in the Holy Roman Empire it became common for the Emperor himself to appoint bishops. In fact, the Emperors even began appointing the pope. This led to a major political and religious crisis known as the investiture controversy.

The events of the contest are relatively straightforward. In the eleventh century, moral reform of the church began to become a popular cause among clerics and devout lay people. Emperor Henry III was a proponent of the reforms, and selected Leo IX, a German bishop and reformer, as the new pope in 1048. Leo's selection began a series of reforms to the church, and one of those reforms was the elimination of simony, or the sale of church office. Leo's reforms continued through the next pope's reign, and then culminated in the figure of Gregory VII who was elected pope in 1073.

Where reformers under Leo had been worried about the sale of office, reformers by the time of Gregory VII were rejecting even the conferring of holy office by a layperson. Gregory tried to promote this, but Henry IV, the current king of the Germans and emperor elect, continued to appoint bishops himself. In 1075, Henry appointed the bishop of Milan, in contradiction to Gregory's decrees. In response, Gregory threatened to excommunicate Henry. A series of escalating conflicts arose between the Emperor and the Pope, until in 1076 Gregory went ahead and excommunicated Henry. Because of dictatus papae, a decree of Gregory's that argued that popes could depose kings, Henry was seen by many in Germany to no longer be king. This led to significant conflict within the Empire, as other members of the nobility rebelled against Henry. At the same time, Henry had been trying to re-solidify his own power in Italy (which was part of the HRE).

Henry made a political play against Gregory by going to Canossa in Italy and doing penance, thus forcing Gregory to lift the ex-communication. This did not solve all of Henry's problems, as there was now a civil war in Germany, but it allowed him to retain Germany and eventually become crowned Emperor. Eventually Gregory VII over-stepped in his reforming zeal and opposition to Henry, and he was deposed by the population of Rome. These were the opening salvos of the investiture controversy, which would continue into the mid-twelfth century. Although it seemed like Henry IV's side of the argument might win, ultimately the right of the pope and only the pope to install bishops was affirmed and followed throughout western Europe.

Some sources

Uta-Renate Blumenthal's The Investiture Controversy: Church and Monarchy from the Ninth to the Twelfth Century

Gerd Tellenbach's Church, State, and Christian Society at the Time of the Investiture Contest

Francis Oakley's The Mortgage of the Past: Reshaping the Ancient Political Inheritance (1050-1300)

The pope and the emperor both claimed the right to appoint bishops and abbots. This eventually led to the Investiture Controversy, which was settled in the Concordat of Worms (1122). The settlement is a compromise, in which the spiritual powers of the bishops and abbots are supposed to derive from the pope, but their worldly powers from the emperor.