Here we go! We dive right in.
Vatican I finds its context in the supposed Era of "Enlightenment" when reason was separated from faith, leading to all the "isms": materialism, liberalism, communism, etc. It can be summarized in calling it modernism. The Church was put on defense and condemned these ideas. In Vatican I, papal infallability was clarified to give more teeth to the defense of the Truth and the rejection of the lies of the age.
Theology developed in different ways. The 20th century hit with all its unique issues: communism, fascism, terrible wars, worldwide discouragement and "nihilism", communication, medial, travel, technology. There were more martyrs in this century than all the other centuries combined.
Pope St. John XXIII was elected to the papacy and three months later announced the opening of the Second Vatican Council, which would be more pastoral, finding new ways to present the fullness of the Gospel of Jesus Christ in the contemporary world in which we find ourselves.
The media caused difficulty in the interpretation, since many people were informed about the council through the lens of the world's media, not the actual texts. Then, there was a group that wanted to go beyond the council, beyond continuity with what was before. However, that did not win the day. Instead, the Church wants us to be guided by a biblical and theological theology centered on Christ and filled with His holiness so that we can be encouraged and courageous in bringing the Gospel to all corners of society.