While the idea of papal infallibility may sound like an ancient or mediaeval concept, it is not. This doctrine was first codified only at the First Vatican Council in 1870. (source)

The doctrine of papal infallibility does not imply that whatever the pope says is always right. For the pope to make an infallible statement, he has to be speaking ex cathedra, in his official capacity as pastor for all Christians, and must make it clear that he is promulgating a binding doctrine of faith. The last time that a pope made an infallible statement was in 1950 when Pope Pius XII issued a dogmatic statement ex cathedra regarding the Assumption of Mary. (source)

When Pope Benedict XVI announced his resignation on February 11, 2013, he told his cardinals, "my strengths, due to an advanced age, are no longer suited to an adequate exercise of the Petrine ministry," and that he had decided to "renounce the ministry of the Bishop of Rome, successor of St. Peter." Because he spoke in Latin, because of the convoluted wording, and because of the significance of what he was saying, several of the 50 cardinals in attendance did not understand what he was saying. (source)