Mormons believe in the "literal gathering of Israel ... and in the restoration of the Ten Tribes," according to the tenth Article of Faith.
The gathering and restoration project has to happen because in the 8th century BCE Assyria invaded Israel and carried off most of the Israelites. Amazingly enough, the Assyrians pretty much managed to capture every member of all of the tribes living in the Northern Kingdom: Asher, Dan, Ephraim, Gad, Issachar, Manasseh, Naphtali, Reuben, Simeon, and Zebulun. Members of Levi who were residing in the Northern Kingdom were also carried away, but other Levites were hanging out with the tribes of Judah and Benjamin in the Kingdom of Judah. Their separation is obviously a very bad thing and needs to be fixed.
This makes for a very exciting game of Where in the World Is Carmen Sandiego?, but with Israelite tribes instead of Carmen.
Back when Joseph Smith wrote the Articles of Faith, much of the world was still an unknown. The tribes could have been hiding anywhere. Many settlers of the American continents believed the tribes would be there, but there was no need to completely exclude the nooks and crannies of Africa, the far reaches of Asia, the Down Under, and the many isles of the sea. The search was on.
Mormons have sent missionaries to every region of the world and have found converts among all peoples, and all we've found are a bunch of Josephites (Ephraim and Manasseh). In fact, the vast majority of Mormons have been assigned to the tribe of Ephraim. It's a little discouraging. Especially when we can't even keep track of the other Josephites.
What's even more discouraging is that, even though many people claim to be the lost tribes, researchers who have sought out the Lost Tribes have found no trace of them anywhere. Where haven't we looked? How in the world can Israel hide from today's DNA analyses? It's like the whole Lost Tribe thing was just made up by some ignoramus in the 7th or 8th century CE. But don't lose hope. They'll show up some day soon!