The Christian Church in its theological sense began shortly after the ascension of Jesus - the account of its beginnings is found in the second chapter of the Book of Acts, and was foretold by Jesus in Matthew 16.18. Theologically, the Church is the Body of Christ made up of all believers in Jesus since its inception on that Day of Pentecost. I personally believe the Bible teaches that it will end its earthly existence at the Rapture, when Jesus comes to gather His own to be with Him in Heaven - not all Christians believe in the Rapture in that manner though, and it is not a fundamental tenet of the faith.