The work will proceed globally. It will result in all "four corners of the earth" being searched to locate and return these scattered "outcasts." They are "outcast" because they lack any identification with Israel. They are "dispersed" because they are everywhere, in all nations, among all peoples. They do not know they have anything to do with the blood of Israel. Until they are converted again, their own bloodlines remain a mystery to them.
Just as they have been scattered, so they must be gathered. When Moses returned to restore keys in the Kirtland Temple, he conferred the authority to bring Israel back "from the four parts of the earth." Any map has four directions. The gathering must reach to all four. Moses' return gave back to mankind the key to do this work of gathering. It began immediately upon his return, and continues to this day. This is why today there are over 50,000 full-time missionaries in every nation of the earth that will receive them.
One of the Restoration's great symbols is in the Temple's baptismal fonts. Beneath every font in every Temple are twelve oxen, symbolic of the Twelve Tribes of Israel. They point in all four directions of the compass, because Israel has been scattered throughout the world; from Africa ("Cush"), to Asia ("Shinar"), to Europe ("Elam"), and the Americas ("isles of the sea). Nephi foresaw the time when the hand of the Lord would be extended into all four directions, gathering again through conversion and baptism the scattered remnants of Israel. The Temple baptismal font symbolizes these latter-day events. They are currently underway. Nephi and Isaiah overlap each other, each telling us to recognize this as the Lord's hand.