When are we in exile in Jewish History? Is it when no Jews live in Israel? Is it when Jews are not in charge of Israel? (For example, we know that when the Babylonians were in charge we had the Babylonian Exile, did this continue under the Persians and then the Greeks; did we have the Persian Exile and the Greek Exile?) What does it say about today? Are we in exile if we have Israel?
Generally, the list of exiles corresponds with the four empires that Daniel envisioned (Daniel 2:37-43 and chs. 7-11). According to most commentators, they are: Babylonia, Persia/Media, Greece (Alexander the Great and his Hellenistic successors), and Rome and her cultural inheritors. Each of these indeed ruled over the majority of the world's Jews in its time. (Note that for nearly half of the Second Temple era - 206 years, according to Avodah Zarah 8b-9a - the Romans exercised greater or lesser direct influence over the Land of Israel, even though for part of that time it had Jewish rulers, first the Hasmoneans and then the Herodians.)
Another view (R. Saadiah Gaon and Ibn Ezra) makes Rome an extension of Greece (which it was, to a large extent, culturally and perhaps ethnically), and the fourth empire is Islam.
Some later commentator (might be Abarbanel - I forget) counters that an empire counts for this purpose only if (a) it took over all of the territories of its predecessor, or (b) it destroyed the Beis Hamikdash. So he explains that Babylonia counts under both criteria, Persia/Media and Greece under (a) only, and Rome under (b) only; the Islamic caliphate, by contrast, failed to meet either one.
Be that as it may, the idea would be that we're still "in exile" until Moshiach comes and the Beis Hamikdash is rebuilt (see Dan. 2:44).
Exile means expulsion from one’s native land by authoritative decree.
Secondly, exile denotes the distance from G-d as the Source of Creation and distance from man shaping his destiny.
Rebbe Shimon bar Yochai says that night represents exile - the banishment of the Jewish nation from its land. Yet, the Shechinah is with us in exile, suffering along with us. Exile typifies departure from one’s natural place. Any exile which the Jewish nation suffers is only temporary and has no ultimate reality. Exile is not a home. Exile is not redemption, no matter how sweet it is.