Like... do they still exist? Yes. There are several thousand who still live in the former lands of the Ottoman Empire, at this point Turkey and the Balkans (including Greece). They continued to speak Judeo-Spanish/Ladino until a generation or two ago (so most people around 50 can speak it, but most people around 30 can't). There's a documentary on it called las Ultimas Palavras, official website here. The websites in Turkish, but the trailer has English subtitles.

These Jews are properly "Sephardi"--Sephardi means "Spanish" in medieval Hebrew, but can ambiguously refer to either just the descendants of those expelled from Spain and Portugal, or not only the Judeo-Spanish speakers, but all Middle Eastern and North African Jews (Arab, Kurdish, and Persian Jews are often called Mizrahi, Eastern, Sephardi can mean either Sephardi or Sephardi and Mizrahi, though then the Jews of Yemen are sometimes included or not included in Mizrahi).

In the 18th and 19th centuries especially, the Jewish communities thrived in the Ottoman Empire, especially these Judeo-Spanish communities (the Jews of Yemen, the Temani, for instance, remained very very poor). There were also small Ashkenazi (Central European) communities in parts of the Ottoman Empire; for instance, Istanbul once had two or three Ashkenazi-rite synagogues (there's one now, but the other building has become an art museum) with the rest being Sephardi-rite. Greece is somewhat more complex because in addition to the large Sephardi (Spanish-speaking) community there was also a large Romaniote (that is, Roman, that is Byzantine, so Greek-speaking) community. There's also some Crimean Karaite Jews in Istanbul. The whole thing is quite mixed.

But the ones in the Balkans were mostly murdered in the Holocaust. Something like 90% of the pre-war Jewish community in Greece was killed during World War II. Salonica, a city that for much of the 19th century was majority or plurality Jewish (and the rest pretty evenly divided between Greek and Turkish) has about 1,500 Jews today.

In Turkey, the Jews gradually consolidated in the big cities, mainly Istanbul, over the course of the 20th century (there are about 10,000 in Istanbul, 1,500 in Izmir, 500-1,000 in Ankara, 40 in Bursa, 10-15 in Antakya, 1 in Edirne) though they were much, much more spread out originally (there were about half a dozen to a dozen towns with Jewish communities in the Izmir Viyalet, for example, around 1900).

In Turkey, there were specific events that made the Jews feel less welcome: the Thrace Pogroms (Trakya Olaylari) of 1934, the "Wealth Tax" of 1942 that targeted minorities, the Istanbul Pogrom of 1955 being some of the big ones. There was migration before that (mainly to Western Europe, particularly France), but those events are generally said to have spend up the outmigration. Once the state of Israel was founded, the Turkish Jews (particularly lower and middle class Turkish Jews) migrated there, especially in periods when Turkey was experiencing economic or political instability and Israel was doing relatively well. So while there are maybe 15,000 Jews in Turkey today, I believe there were maybe 60-80,000 in Modern Turkey at the end of the Ottoman Empire (the vast, vast majority Spanish speaking), perhaps as many in Modern Greece, and more scattered throughout the Balkans as far as Bosnia. Bulgaria had a large community of Sephardi speakers, but I just don't know much about their history.

Look at this translated chart of literacy rates from the 1945 Turkish census (coincidentally, at the very point when most of the rest of the Judeo-Spanish speaking communities of Europe had been destroyed by the Nazis). The original Turkish census listed the language as "Jewish", I believe, but that meant Judeo-Spanish. The English translator was not familiar with it, and rendered it as "Yiddish". Still, notice that there were still more than 50,000 native Judeo-Spanish speakers--most literate--in Turkey in 1945. Most of these Jews or their descendants ended up in Israel, with only a minority staying in Turkey, Greece, Bosnia, Serbia, and Bulgaria. Most of the Jew who stayed in Anatolia and the Balkans and most of those who moved to Israel ended up not transmitting Judeo-Spanish to their children in last quarter of the 20th century.