Yesterday's post on the long and geographically vast history of Aramaic and Syriac treated it as a fascinating historical artifact. It is nearly that, but not quite yet. Both Western and Eastern forms of Aramaic are still spoken. The latter is spoken by far more people. The former is better publicized. Let's deal with it first.
Modern Western Neo-Aramaic, as the linguists call it, is spoken today in only three villages north and west of Damascus: Ma‘alula, Bakh‘a, and Jubba‘din. Ma‘alula is the best known, a dramatically situated town perched high on the slopes of the Anti-Lebanon range, with two ancient Greek Catholic monasteries; it does (at least when Syria is not in revolution) a brisk tourist business since it's scenic, near Damascus, and promotes itself as "still speaking the language of Jesus." Western Neo-Aramaic descends from a version of Christian Syriac that was probably rather different from the language of Jesus, which was doubtless closer to the Aramaic in which the Jerusalem Talmud was written a bit later, though both the Gospels (when Peter is accused in Matthew 26:73 of being Galilean because "even your speech betrays you") and the Talmud note that Galilee had a very distinctive dialect.) But yes, it's closer to the language of Jesus than any other spoken language today, since the more widely spoken varieties of Eastern Neo-Aramaic are very different, At best, 15,000 speakers of the Western variety survive.
Western Neo-Aramaic, despite its limited survival in only three towns, has a distinction that, so far as I know, none of the various Eastern survivals do. Many of the speakers are Muslim. Bakh‘a and Jubba‘din are overwhelmingly or completely Muslim towns. All speakers of Eastern Neo-Aramaic are non-Muslim: Christians of the Assyrian Church of the East or the Chaldean Catholic Church (in Turkey, Iraq, and the Diaspora, Jews (especially Kurdish Jews, though a few other groups exist), or Mandaeans (mostly in Ahvaz, Iran today; Iraqi Mandaeans speak Arabic).
Even odder, the Muslims of the three Aramaic-speaking towns apparently Islamized without Arabizing. Like other peoples in the core Middle East who became Muslim without adopting Arabic, such as Kurds and Berbers, their mountain fastnesses helped isolate and preserve their language. But unlike Kurds and Berbers, they were near the capital of the Umayyad Caliphate, Damascus. (Other religious minorities such as the Samaritans retained Aramaic speech longer than their neighbors and still use it liturgically.)
Oddest of all, the linguists say the least-Arabized of the three villages, retaining the most conservative Aramaic of the three, is Bakh‘a — which is entirely Muslim in religion.
Eastern forms of surviving spoken Aramaic are less well known because they do not have Ma‘lula's claim of "speaking the language of Jesus" (though they do in the broader sense); there may be half a million or so speakers of Assyrian, Chaldean, Mandaic and other forms. They differ a lot among themselves. They're tomorrow's post.