The Church has existed in unbroken succession through 2,000 years of Christian history. St Paul calls the Church the ‘body of Christ’ (Eph 1:22-23). As a body, she has an ordered structure and a visible unity. As Christ’s body, she also has a human and divine nature (ccc. 771).
The main way in which we know that the Catholic Church today is the Church founded by Jesus Christ is the continuity of the Church since the time of the apostles. This claim does not imply an assertion that the Catholic Church today exactly resembles that of the early Christians, but that the Catholic Church today has developed in a continuous manner from the early Church. This development has an organic coherence, like that of a plant growing from a seed. This coherence and continuity of the Church through history can be seen, first, from the way that even early Christian writings refer to the ‘Catholic Church’, the word ‘catholic’ (katholikos), meaning ‘universal’, ‘complete’ and ‘whole’. In approximately 107 AD, for example, St Ignatius, who was bishop of Antioch, wrote, “Wherever the bishop appears, there let the people be; as wherever Jesus Christ is, there is the Catholic Church” (Letter to the Smyrnaeans, 8). St Ignatius, who links the presence of Jesus Christ to the Catholic Church in this text, refers elsewhere to the Church in Rome as ‘presiding’ over love. A second mark of continuity is the structure of Holy Orders: St Ignatius also refers to bishops, priests and deacons, essentially the same structure of Holy Orders that exists in the Catholic Church today. Furthermore, the office of Bishop of Rome, who is usually referred to today as the Pope, is not a modern invention but can also be traced back to the early Church. In Scripture, Peter is singled out as having a special role among all the apostles (cf. Mt 16:18) and early Church writings emphasise the continuation of this office by his successors. In 180 AD, St Irenaeus records that the Church of Rome had maintained a perpetual succession of bishops from the time of its founding by the apostles Peter and Paul and that it is essential for every local church to be united with the Church of Rome, on account of its ‘pre-eminent authority’ (Against Heresies, III.3). Uniquely in the world today, however, only the Catholic Church still maintains this communion with the Bishop of Rome. By contrast, the vast majority of the other Christian communities today, now numbering many thousands, tend to fragment easily and are generally much less than five centuries old. So notwithstanding the many moral and other imperfections of her individual members, there is, therefore, a unique, organic continuity between the Catholic Church today and the Church of the early Christians.
In the nineteenth century, John Henry Newman developed detailed arguments that identified the Roman Catholic Church with the early Christian Church, a conclusion that eventually led Newman himself to be received into the Catholic Church. His Apologia Pro Vita Sua and Lectures on Certain Difficulties Felt by Anglicans may be helpful to those who wish to explore the historical and theological issues in detail.