The Roman Catholic, Eastern Orthodox, and Anglican Churches hold that apostolic succession is maintained through the ordination of bishops in unbroken personal succession back to the apostles. The Roman Catholic church notably denies that the Anglican Churches practice valid apostolic succession. For the Eastern Orthodox (and Catholics?), it also means that their teaching today is the same as or is in harmony with the teaching of the first apostles.
Most Protestant churches maintain that their bishops and priests, although they do not trace a succession of ordination back to the apostles, are the spiritual successors of the apostles by faith the inspiration of the Holy Spirit (an extension of the Lutheran doctrine of sola fide).