there were no royal houses in the first century anymore. The northern dynasties were wiped out in 720BC when the assyrians conquerend the land, killed/deported its kings and deported part of the population. Its last king was Hoshea.

The kingdom of judah followed a similar fate in 586BC when jerusalem and the surroundings fell to the babylonians. Its last king was Zedekiah, who revolted to the babylonians who in turn besieged jerusalem, captured him, slayed his sons, blinded and deported him to babylon, where he died.

If by royal house you mean the herodians, Agrippa II was the last of them and he was pretty much alive during the destruction of jerusalem and shortly thereafter but at that point romans had firm control of it.

If you want to know more about the davidic royal house I'd suggest this mooc

https://www.coursera.org/learn/jerusalem

which is the mooc version of this volume

https://www.eisenbrauns.com/ECOM/_4NS0P016P.HTM

warning: academic archaeological publication, so be ware it won't be a "fun" read, but will cover the question of the davidic royal house and the shift of power quite well. Or, as weird as it sounds, you could just read the bible passages on the matter because they are quite accurate, being written by first hand witnesses.

/u/stoicismus covered the details pretty well. But I thought I'd add some additional detail.

The Herodians - Photius recorded that Agrippa II lived till 100 CE. And that seems plausible. We have an official government weight that is inscribed as having been cast in his 43rd regnal year, which would have been 98 CE. His territory moved around quite a bit, and was subject to the whims of the Roman emperor. At the time of his death it was a small territory in modern Lebanon and Syria. No one mentions any children of his, and his kingdom was reabsorbed by the Empire. That doesn't mean he didn't have children. But with Jerusalem depopulated, the temple destroyed, and the surviving Jews scattered, there just didn't see to be a need for a Jewish king to maintain order over the Jews.

And for their part the Jews didn't seem to have fond memories of either the Hasmoneans or the Herodians. The wanted a messiah, a Davidic King, who would restore full independence and glory. They were done with hellenized/romanized client kings to larger states like the Seleucids or Romans. So if Agrippa II had any children, there certainly wasn't popular support to put one on a throne. We call Agrippa II the last Herodian not necessarily because he was (though he may have been), but because no one seems to have cared a whit about the dynasty after him.

The Davidians - Officially the dynasty ended in 597 BCE. But unlike the Herodians people loved the Davidic dynasty. So there are Jewish families today that have maintained millennia long traditions of Davidic descent. Likewise as an ancient anointed holy King, a lot of European royalty claimed eventual descent from David. Even today, Elizabeth II of the U.K. has David in her official family tree. 6th century BCE genealogies weren't well kept, so all claims at royal descent eventually break down to oral claims. It's impossible to certify which if any of them might actually be true. But David and other Israelite Kings are infamous for their large numbers of wives and concubines. It's certainly possible that a cadet branch of the family survives. Assuming of course that David himself actually existed. We know that there was a 6th century "House of David." We don't know for certain that they were actually descended from an actual 10th century King David. He may be entirely mythological.

Curious, is "Israeli" acceptable terminology for this context? I thought "Israelite" was preferred for pre-1948 discussion, but I know very little about this subject.

/u/Stoicismus and /u/quickspore cover the idea of the Royal House, but that's not the end of the discussion on Davidic descent. There are Jews who have claimed descent from David, in both the present and past.

An important point is that the Messiah must come through David. The New Testament, therefore, goes out of its way to establish Davidic descent for Jesus (confusingly, this is done through Joseph, Jesus's legal but not biological father, in the two books that seem to be trying to establish the connection; Matthew is fairly unambiguous in this regard, though one reading of Luke argues that Luke is giving Mary, rather than Joseph's, family tree, which would make more sense in the case of a virgin birth).

There have been likewise active claims of Davidic descent in the Jewish community (especially in the Hasidic world), many of which are centuries old. In 2006, for instance, there was a sort of Davidic family reunion organized in New York. Here's the Forward article on it. Here's an article for the Orthodox Moment Magazine, which details the traditional claims of Davidic lineage:

Male descendants of King David ruled Israel until the Babylonians conquered Jerusalem in 597 BCE, and Jews scattered. Some managed to stay in Palestine, others fled to Egypt, but the victorious Babylonians took most of the nesi’im—the princes of the Davidic line—to Babylon. There, the King David line continued: Princes of the House of David were appointed by religious leaders to govern the Jewish community. This person was called Rosh ha’gola, which translates as “head of the exile” or exilarch. Fraught with behind-the-scenes political infighting, the position survived the Arab conquest of Baghdad but came to an end when the last exilarch, Hezekiah, was imprisoned and tortured to death in 1040 CE.

Descendants of the exilarchs and other nesi’im fanned out across Mesopotamia, the Levant, Egypt and the Mediterranean basin in search of new lands in which to practice their faith. Some stayed in Spain, Portugal and Italy, and from there migrated to Europe. Like other Jews, they followed varying routes to modernity, separating into Ashkenazi, Sephardi, Mizrahi and other groups. Some families, especially rabbinic ones, kept careful track of their pedigrees, passing the tradition of royal descent from generation to generation. But through the centuries, plagued by perennial migrations and persecution, the vast majority of King David’s descendants, a number estimated to be in the millions, lost knowledge of the line…

The article goes on to detail many important rabbis and figures who had apparent Davidic descent, including the founder of Hasidism the Baal Shem Tov, my favorite Hasidic Rebbe Nachman of Breslov, without doubt the most famous Hasidic Rebbe of the 20th century Rabbi Menachem Mendel Schneersohn the 7th Chabad Rebbe, and comedian Jerry Seinfeld.

Often related through marriage and with intertwining family trees, [these rabbinic families] generally trace their lineages to great 18th and 19th century rabbis such as the Ba’al Shem Tov, Rebbe Nachman, the first Lubavitcher rebbe and Saadya, the Gaon of Vilna, or further back to 16th century luminaries such as the Maharshal in Lithuania (Shlomo Luria) and the Maharal of Prague (Judah Loew ben Bezalel).

Usually, these chains of rabbis are linked to earlier chains of rabbis back to Rashi, the perhaps the first very important post-Talmudic rabbinical sage.

So how do we know that these great rabbis of Eastern Europe were descended from King David? Tradition has it that they are all descended from the royal house through Rabbi Shlomo Itzhaki, known as Rashi, the great biblical commentator born in 1040 in the French city of Troyes. “You have stations along the way,” says Abraham Twerski, a psychiatrist and rabbi descended from the Hasidic dynasties of Chernoble and Sanz. “[The Twerskis] have a direct line to the Maharshal,” he says. “It is known that Maharshal had a direct line to Rashi, and Rashi to Rebbe Yohannan HaSandlar, one of the major authors of the Talmud and a shoemaker by profession. HaSandlar was known to be descended from King David.”

Sephardic claims are similar, but tend to go through the last exilarch Hezekiah, who was roughly a contemporary of Rashi's, or (among Syrian Jews) through "Josiah Hasan ben Zakkai, brother of the exilarch David (?917-940)".

Now, beyond the obvious issues of Davidic descent being different from the House of David (which implies that it is or at least could be a ruling house with a continuous male line--among most claimants, the descent goes through daughters at some point, meaning genetic testing base on y-chromosomes, as has bend done bolstering claims that many Cohen families share common descent, apparently from the High Priests of the Temple Period, can't be done), how serious we should take these claim isn't perfectly clear.

According to the late David Einsiedler, who wrote in the scholarly journal, Avotaynu: The International Review of Jewish Genealogy, “Careful examination of all available sources leads to the inescapable conclusion that there is no complete, reliable and positive proof of claims of descent from King David, whether via Rashi, Judah Loew the Elder, or any of the other families claimed. There are at present no known sources that could fill the gaps or set the record straight. It is possible that there may be actual descendants somewhere, but at present, no one can produce sufficient and unquestionable proof of this claim.”

And moreover, a long time passing means quite simply that if anyone is related to David, a lot of people are.

“Since it is 3,000-plus years since David, there is at least an 80 percent chance that any Jew is a direct descendant of King David,” says Yale University statistician Joseph Chang in a 1999 article in Advances in Applied Probability.

Since genetic evidence seems to bolster many of the traditional claims Cohen of descent from Temple high priest (or, again, at least many of them widely dispersed around the world share common descent through an unbroken male line from someone--remember Y-chromosomes are uniquely passed directly from father to son with minimal genetic change), I think these claims of Davidic descent shouldn't be dismissed out of hand. However, on the other hand, because of the great time periods we're talking about, any one individual claim of descent can't ever fully be confirmed.

As far as I know, there has been no mention of a Jewish royal house from the time of the Herodians. While one can safely presume that their descendants are still around, especially in the female lineage, there is no way for them to prove it as the information has been lost. DNA evidence is not available.

This is one of the irritating features of history. As another and unrelated example, it stands to reason that there are descendants of the Hunnic royal lineages in Europe. But we do not know who they are, as human information systems only last so long. Expecting papyrus, parchment, paper, movie film, or even modern software to last indefinitely is not reasonable, and even if it lasts, if the language is lost, it is hard to decipher (as in the case of the Etruscans).

There are families today, that are descendants of the Exilarchs, and are of the House of David. The Dayyan family of syria is one.

Did King David even exist? If I remember correctly, Finkelstein's The Bible Unearthed argue he didn't and at his alleged time Jerusalem was simply too small.