One of the great Christian goals has been to convert the entire world. Certainly, the faith has been very successful. It started small and became one of the world’s largest.
Will it achieve it goals of converting the entire globe? In a word, no. The phenomenal success of Christianity took place under circumstances different from what exists today. Some of the big numbers came from Africa where local religions put up little competition. Both Christianity and Islam filled up the continent.
A Christian research organization, the Center for the Study of Global Christianity (Gordon-Conwell Theological Seminary) provided a realistic look at the future of the faith. It pointed out that the fate of religions rests on the number of births and the voracity of the competition. For Christianity, births are falling in its long standing base areas and will soon fall the in the areas where its growth has been strong.
Non Christian areas are now occupied by Islam or Hinduism. The faith has had little success trying to establish beach heads in regions where these other faiths are already established. Nearly all missionaries are now sent to regions where Christianity has been for a while.
Even though more people are leaving the faith than converting into it, population growth will keep world wide numbers from falling for some decades. This, though the percentage of believers will fall.
Christianity, and other faiths, can only life in certain cultures. When the cultural opportunities are exhausted and the birth rate falls, growth is over.
[A link in comments discusses this further.]