Wherever Jews live.
History:The prophets had constantly warned the Israelites
that ignoring the Torah would result in exile.
1) Around 2600 years ago, the Assyrians forcibly exiled the Ten Israelite tribes to points unknown. A small percentage of each of these tribes is still among us, but most of them were exiled and didn't return.
3) In 68 CE, the Romans destroyed the Second Temple. The Romans did not force the Jews out of Judea in a single expulsion. Rather, the Romans expelled them from Jerusalem only; and the rest of Judea lost its Jews slowly, over a period of centuries, as living there became too harsh. Even then, we have records of Jewish communities who lived in Judea (Palestine) during the entire period of the last two millenia.
Those Jews who left Judea went to southern Europe, North Africa, Arabia, the Near East, and (slowly) further afield (especially throughout Europe).
The diaspora (scattering) was difficult for us:
1) Because certain mitzvot (such as those related to agriculture in the Holy Land) now became suspended for the duration of the exile.
2) Because of the impediment to communication between the various communities. This could lead to the development of rivaling groups, each claiming to be authentic.
3) Because the Jews were now a minority among other nations, who were sometimes quite hostile.
4) Along with the Torah, the Land of Israel (Judea) and the Holy Temple had been central to Judaism. It now was to be seen whether Torah-observance could be maintained on the high level that those ideal factors had been conducive to.
How did the diaspora affect the Jews?
To a certain extent, the diaspora caused the various Jewish communities to take on minor aspects of their host countries.
The religion itself was affected little, if at all, since all Jews share the same Torah and Talmud, and differences within halakhah (Jewish laws) are relatively small. In addition, the Jews were dissuaded from assimilating because the Romans were the polar opposite of Judaism; plus the fact that some of their greatest historians spewed diatribes of hate against the Jews.
See also the other Related Links.
Currently there are few - if any - Jews in most Arab countries, but until 50 years ago there were thriving communities there also.
2. All over the world, through exile, migration, and missionary work (particularly in Ancient History and the early Middle Ages).