Continuing on my attempt to explain all Jewish history and sectarial breakdown in 2 posts (which I suppose is somewhat like the classic scenario from the Mishnah where someone comes to the great sage Hillel and requests him to explain all the Torah while he's standing on 1 leg) (part 1 one)...
Picking up where I stopped previously, there was basically 3 divisions, one group who was exiled east and lived in (what's modern day) Iraq, Iran, Afganistan, Yemen, etc, one who lived in northern Africa (what's modern day) Morocco, Egypt, Tunisia, Libya, etc, and one who lived in northern Europe. (Previously I had lumped the non-European groups together, Reb. Natan commented "Sephardim refers specifically to those who lived in Iberia (Spain) and fled the Inquisition. The Jewish communities of North Africa and Iran/Iraq are by and large NOT Sephardim, despite the colloquial term used in Israel. They are Edot Hamizrach.") However, as he notes, both are today commonly referred to as Sepharidm.
Now mystical practices as part of Judaism was a regular thing. Mystical prayers and references were incorporated into the regular prayer set and household or community mystical practices were not unusual. Further, Jewish mystics, kabbalists (mekubalim in Hebrew), were also not an unusual thing.
However, as the Jews moved north several things happened (over a few hundred years) that changed this. First was a simple environmental situation. The northern towns and cities were smaller and couldn't support as large of a concentrated population. Therefore, the Jewish population spread out among the towns and villages in search of a livelihood. But for a community to support an experienced rabbi, a Jewish school and other major Jewish community needs requires sufficient concentrated population. It didn't exist in the villages, and Jewish education declined. There became an 'ignorant' or simple Jewish class of people. Somewhat in response to this, Jewish scholarship in the cities took on a almost feverish or frantic intensity. There also grew some corruption and nepotism on rabbinic posts, with some village and town positions being bribed into (bribed to the local landowner). This resulted in a decline in trust of the village Jew in the rabbinic establishment and scholarly class.
In parallel with the above arose two mystics (again in the north) who went off the path and drew thousands after them. As it says in the Yom Kippur prayers, 4 (great) rabbis entered the sphere's of heaven, one died, one went insane, one became an apostate (turned on his faith), and one came in peace and left in peace. These mystics declared themselves to be messiah's and drew many after them. Their end was bad, and the results were bad for the Jewish population in general.
In response, the northern rabbinical establishment declared that mystical practices and mystical study was only appropriate for the most senior, learned and well grounded rabbinic scholars. No others were to be tolerated being involved with the mystical in the slightest. Mystical practice was banned. Further, a somewhat fire and brimstone approach was taken to the ignorant classes, to keep them away from the terrible negative potential of such things as had happened.
In response to this the Jewish mystics of the north went underground. Hidden societies of saintly mystics existed and might quietly approach a student or scholar for their interest in learning or joining, but otherwise they were out of sight. One such group had a somewhat different perspective and believed they had a responsibility to the general Jewish population to uplift and inspire them. They quietly and in small groups traveled from village trying to raise spirits and teach how special everyone is to G-d.
This group was led generation after generation by a leader known as the Baal Shem, literally the Master of the Name, meaning a saint and mystic who used the great power-names of G-d to help people out (just the kind of thing the rabbinic establishment was worried about being misused). Examples of such leaders are Rabbi Adam Baal Shem and Rabbi Eliyahu Baal Shem.
About 400 years ago this group encountered a young pious dedicated man who joined their group and their purpose. After being with them for about 10 years, he became their leader. He was known as Rabbi Israel...Baal Shem Tov (the master of the good name).
When he took over leadership, he decided to change the direction of the group. Rather than hide and quietly try to help out a bit, he felt that the morale situation of the village Jews was dire and it was urgently necessary to teach them the tremendous love and value of every soul to G-d, that sincere prayer and a sincere relationship with G-d was possible for everyone, not just the scholarly class. Further, even those with limited education could understand basic mystical concepts to reinforce their connection with G-d and strengthen their prayers. Finally, by stamping out mystical practices he felt that the rabbinic establishment had also slightly deviated from the preferred historical traditional practices.
So he set about with the group of mystics to teach and lead people in a slightly different direction. The Baal Shem Tov's followers became known as Chassidim, the path he taught is Chassidus.
His movement grew like wild fire. The rabbinic establishment was aghast, this was exactly what they were worried about. Here was another mystic proclaiming mystical teachings, using mystical powers, and suggesting changes to the tradition Judaism of the area. It had to be stopped and stamped out at all costs! This philosophical battle lasted several hundred years. It was incredibly painful at the time, sometimes with families splitting up over it. However, the results were amazing, in that certain excessive fervor of the chassidim was curtailed in light of the opposition, to make their arguments the chassidim found themselves forced to adopt an intense level of traditional Jewish scholarship, and the establishment found itself forced to examine, expound upon and back off (slightly) on the mystical studies ban.
Upon the Baal Shem Tov's passing, a very scholarly mystic named Rabbi Dov Ber took over as leader of the growing chassidic movement. His top students and disciples, as well as some of the Baal Shem Tov himself, spread out to different areas to spread chassidus. Each one of these became a Rebbe, a grand rabbi or leader of a chassidic sub-sect. The places they spread out to are the names of the chassidic groups. (Ok critics, this is somewhat of an oversimplification I know and sometimes several generations were involved before the names took hold.)
Today there is maybe a dozen large chassidic sub-sects and 50-75 small ones. The chassidic philosophy of the different sub-sects is somewhat tuned to the target populous of the original landing place of the sub-sect leader. One's a bit more intellectual, one's a bit more emotional, one's a bit more leader oriented, one's a bit more self-effort oriented, etc.
These are the chassidic movements / Jewish sub-sects you may hear about today: Satmar, Lubavitch (Chabad), Breslov, Munkatch, Bobov, Viznitz, Tzanz, and others (sorry, these are just off the top of my head). Sometimes there are splits over generational changes in leadership, sometimes mergers. The splits have lead to some new namings, even American ones, such as Bostoner (who do indeed live in Boston) and Pittsburger (who live in Ashdod, Israel). All of the chassidic movements have a leader, a grand rabbi or Rebbe, with two exceptions, Breslov had only 1 grand rabbi originally and none since, and Lubavitch, who's 7th grand rabbi left this world in 1994 with no successor being named or accepted.
In the case of the large movements, they tend to congregate in different major communities in a few places throughout the world. In the case of the small ones, the whole movement tends to be in 1 place. Lubavitch is an interesting exception which, under the direction of the last grand rabbi, went back somewhat to the original roots of the northern hidden mystics and instructed his followers to send out emissaries to all Jewish communities in the world, to uplift their local Judaism. Therefore, you will find 'Chabad' houses, a local Lubavitch chassidic presence, literally world-wide.
BS"D - בסיעתא דשמיא