What happened to the Aseres HaShevatim? Where are they now? Are they in 10 different locations? Do they still know they are Jewish?
The Gemara (Yevamos 16b-17a) cites a couple of opinions that bear on this:
"If a non-Jew nowadays performs kiddushin with a Jewish woman, we have to be concerned that these kiddushin are valid [and they need to be dissolved with a get], since he may be from the Ten Tribes." [The Gemara goes on to qualify this: it applies only if he's from the areas where the Ten Tribes were exiled, as listed in II Kings 17:6.] The implication, then, is that they assimilated among the local non-Jews.
The people in these locations are considered out-and-out non-Jews. Even though the exiled Jews there included women [whose children ought to be considered Jews, as per the usual rule that Jewishness follows the mother], either all of these women became infertile, or there was an explicit ruling by the halachic authorities of that time that they were to be considered non-Jews. [How exactly that would work - don't we always say that a Jew remains a Jew no matter what? - is the subject of a lot of discussion among the posekim.]
On the other hand:
Already shortly after the Ten Tribes seceded and formed their own kingdom, we find members of those tribes - those who wanted to continue being able to worship Hashem in the Beis Hamikdash - moving south to the Kingdom of Judah and remaining there (II Chron. 11:16).
Some 90 years after the exile of the Ten Tribes, the prophet Yirmiyahu (Jeremiah) brought a lot of them back to the Land of Israel, where they became subjects of King Yoshiyahu (Josiah) of Judah (Megillah 14b, Erchin 33a). They shared the fate of the Judeans a couple of decades later, in being exiled to Babylonia, but they retained their identity as Jews.
Of the 42,360 people who left Babylonia to come to the Land of Israel and build the second Beis Hamikdash, about 13,000 were from the Ten Tribes (Rashi to Ezra 2:64, quoting Seder Olam Rabbah).
According to some opinions, the Ten Tribes will be restored along with the rest of the Jewish People when Moshiach comes (Sanhedrin 110b). Rashi there (ד"ה כיום הזה) cites his teacher as saying (if I'm understanding him correctly) that even R' Akiva, who says that they are gone forever, is talking about the original exiles, but that even he would agree that their descendants have a future as part of the Jewish People.
Yechezkel (Ezekiel) describes how the Ten Tribes (whom he calls "the stick of Joseph... and his fellow tribes") will rejoin the tribes of Judah and Benjamin ("the stick of Judah") and they will re-form one kingdom (37:15ff). He also describes the borders of the land that will be re-divided "for the twelve tribes of Israel" (47:13), and gives the details of how the tribes' lands will be arranged (48:1-7 and 23-28). So all twelve tribes will indeed exist as defined units in the era of Moshiach.