The Goteijusantai is the oldest, and only, collection of Shinigami in any dimension. Shinigami are trained by the Shinou Academy, and placed into a division, in a bit of a military-like structure, and exist to oversee the flow of souls from one world to the next, as well as protect living humans from Hollows. The Goteijusantai has, officially, thirteen divisions, with two somewhat-independent off-shoots; the Onmitsukidou, or Special Operations Force; and the Kidoushu, or the Kidou Corps, which specialises in the research and teaching of Kidou magic. As of now, the Onmitsukidou and the Nibantai, or Second Division, are led by the same Captain and Lieutenant, effectively marrying the two together.
The Ichibantai are the enforcement division. At one time, they enforced the laws set down by the Central 46, but with the Central wiped out, the Sotaichou has opted to replace Central, the Seireitei's government body, with a council comprised of the divisions' captains, called the Council of Thirteen. The captain of the first division, the Sotaichou, leads the entire Goteijusantai.
The Nibantai have been married to the Onmitsukidou, or the Special Operations, for so long, that no one really remembers what they did before this arrangement. As such, the Nibantai is generally integrated with the Onmitsukidou, and the Captain of the Nibantai is also the Commander of the Special Operations Forces. They handle very sensitive and important message delivery, dangerous criminal handling and detainment, and at one time were under direct command of the Central 46; this is now the Council of Thirteen.
The only division to focus entirely on it, but not the only one to handle it overall, the Sanbantai are entirely focused on living world defence. Most Goteijusantai patrols in the living world are from Sanbantai, and they take two weeks out, one week in the office, and one week off entirely. The schedule is a bit rigorous, and doesn't leave much room for a social or family life, so those that join Sanbantai tend to have neither.
The Fourth Division are primarily healers; from intensive care, to general wellness, to field healing and emergency services, the Fourth Division handles it all. Oh, they also keep your office stocked with paper and staplers. There are several different, focused units within the Fourth Division, which handle specific things, such as heart-related problems, an emergency ward, an intensive care ward, and so on.
Traditionally led by the noble Jeon family, the Sixth Division houses, tracks, and maintains the Great Archives beneath the Seireitei. Every important event that happens within the Seireitei, from Hollow attacks, to emergency living world situations, to crimes, births, marriages, and deaths, are recorded and stored in the Great Archives.
When something goes amiss or awry, and no one seems to have any answers, it is the Kyubantai that answers that cry for help; the investigation division looks into crimes, trouble, and other sorts of dangerous situations and events, in order to find the truth and better inform the Seireitei how to approach and handle any given situation. Unfortunately, this means they are the first in unknown situations, and often take the brunt of lacking knowledge.
As the melee combat division, the Eleventh Division essentially spends their time honing and perfecting their Zanjutsu skill, and are often found sparring one another. The division is usually the first on the front-lines, perhaps after eighth, ninth, and tenth, but they are also often the last ones off the battlefield. The division used to be quite unruly, but these days, the new Captain's managed to calm their battle-thirst a bit.
Where the Fourth Division often deals in medical research, the Twelfth deals in scientific research, and develop new technologies, and improve on existing ones, in order to make the lives of the Goteijusantai, and sometimes the Seireitei as a whole, much easier. Sometimes they can be a bit sketchy with their morality and sense of ethics, but none can deny that their inventions are quite the impressive improvements.