Where can I find a discussion about the roots of modern nations, in the Umos Haolam mentioned in the Torah and Chazal?
Aside from those mentioned already, there are quite a few references to peoples, or places, in Tanach that have been identified with modern nations:
Tzarefas (Obadiah 1:20) = France
Sepharad (ibid.) = Spain (whence the term "Sephardim")
Ashkenaz (Gen. 10:5, et al) = Germany (whence "Ashkenazim")
K'naan (ibid. v. 6, et al) = the Slavic nations (Rashi refers in several places to the Slavic languages as "lashon K'naan")
Philistines (ibid. v. 14, et al) = Berbers (Seder HaKabbalah of the Raavad consistently refers to them as such)
Sinites (ibid. v. 17, et al) = China (Daas Soferim to this verse, by R' Chaim Dov Rabinowitz)
Amalek (ibid. 36:12, et al) = Germany (attributed to R' Yosef Chaim Sonnenfeld in the name of the Vilna Gaon)
- though none of these really have halachic significance, as far as I know.
Many different views of the matter are described here:
Too long and complicated for me to summarize.
There are numerous Biblical place-names which we're pretty sure we can identify (tzarfas, sfarad, etc.); but as far as peoples go:
Many halachic sources use the terms "Ishamaelite" or "Hagarite" to mean Muslims. E.g. how halacha views Islam and its practices. That's the terminology.
Any halacha regarding actual ancestral peoplehood (e.g. marrying a Biblical "Egyptian", "Moabite", "Canaanite") was rendered moot thousands of years ago, as Sanhereb of Assyria mixed everyone up. That means halachically today, there's just one giant category called "generic non-Jew." For instance, a non-Jew of any extraction whatsoever can marry into the Jewish mainstream if s/he converts.
Many rabbis (and laymen) have sought to understood historical events in light of Biblical references, e.g. trying to understand the Nazis by looking to the Torah's commandment to remember Amalek.
- Some then go further by claiming, for instance, that the Germans are actually descended from Amalek. If that helps your religious life, great; if not (or you're skeptical), that's okay too. It's of no halachic significance today, nor is it one of the 13 Principles of Faith, or any other major belief that's part of normative observant Jewish thought.
- In fact, (ברוך שכיוונתי, thank you Yitzhak!), Rav Wozner writes similarly (Shevet HaLevi 5:149):
Regarding the question on the tradition of the Vilna Gaon that the Germans descend from Amalek; if regarding their evil actions, certainly they are similar. But to [actually] judge in today's age is difficult, as ... Sanherib mixed up all the nations ... and if so, regarding an Amalekite, it is certain we don't know.
The Gemara in Meggilah List a nation called GermaMia and the Vilna Gaon corrected the text to read “GermaNia" A plain reference to Germany and this was way before the Holocaust.
Just to explain Alex's refrence about Reb Sonnenfeld. He was once asked why he did not go out to meet the German (Prussian) King to make the Bracha on seeing a King.The Halacha is you should go out of your way to make a Bracha on the king of the other Nations. But he refused to meet with Kaiser Wilhelm of Germany who visited the Old City because he believed that the Emperor was a descendant of the nation of Amalek.His refusal was because he is reported saying he has a Kabbalh from the Gra that Germany is Amalek and you dont Make A Bracha On the King of Amalek