After Yisro brings Tzipora and Moshe's sons back to him at Exodus 18:2-5, they are not mentioned by name again in the Torah. Divrei Hayamim (Chronicles I 23:14 et seq.) lists their male descendants but only tells us that they were normal leviim. Do we know anything more from the Oral Tradition?
Apparently it didn't go great for them. Moshe's calling took its toll on his wife and kids. In the book of Judges it tells of a fellow looking to open up an idol-worshiping temple, but he needs a priest; he encounters a job seeker who's just a plain Levite --eh, good enough! And this Levite's name is "the son of Gershom, the son of MeNashe" (with a funny-shaped Nun). Our tradition says this funny nun is the verse's way of covering up that in fact it was Moshe. So his grandson wound up as an itinerant-priest-for-hire.
The nun is hanging, not large.– Double AA ♦Feb 5, 2013 at 16:15
The question asked about Moshe's descendents (plural). How does this source suggest that "it didn't go great for them" (emphasis added)?– FredFeb 5, 2013 at 16:32
@Fred, correct, we only know about this one. We do know that his offspring otherwise never got a mention, so they apparently didn't become leaders. It's also notable that Aharon was succeeded by his son, but Moshe wasn't.– ShalomFeb 5, 2013 at 17:48
@Shalom Over 99% of the Jewish people were not mentioned by name, including members of Sanhedrin and the like. It seems to me that we cannot safely draw inferences about Moshe Rabbeinu's descendents from a lack of information.– FredFeb 6, 2013 at 6:20
I heard that this granson of Moshe lived a very long time because he did things to undermine his idolatrous job, and he was hired by David, who convinced him to do Teshuva, with the incentive of a job in the Temple treasury. Then Shlomo fired him, and he went back to bad ways. Some say he was the false prophet of Melachim B 13:11-32, but did a permanent Teshuva on receiving a true prophecy and seeing what happened to the true prophet he deceived. Sep 23, 2014 at 17:54
According to Bavli Berachot 7a, Moshe’s descendants surpassed the number of (male) Jews who left Mitzrayim, i.e., more than 600,000.
There is mention somewhere that a descendant of Moshe was in charge of finance at the time of David HaMelech. Interestingly, if you read Benjamin of Tudela, in his travel to Bavel (Iraq) in the 12th century, there were 2 Levi dayans (Judges) that has yichus going back to Moshe Rabeinu.