Shitennou (四天王; Four Heavenly Kings) was the title of Queen Beryl's four generals: Jadeite, Nephrite, Zoisite, and Kunzite. They were each named after a different stone. Jadeite and nephrite are two varieties of jade; zoisite's other name is blue tanzanite, and kunzite is a type of spodumene.
In the anime, the Shitennou were simply Beryl's generals. There was a lot of rivalry between them, especially between Nephrite and Zoisite, which ended in Nephrite's death. Jadeite and Nephrite were picked off quickly, while Zoisite and Kunzite lived longer, thanks to their scheming. Beryl valued them as long as they were successful, then simply discarded them.
In the manga, before becoming Beryl's generals, the Shitennou were the guardians of Prince Endymion, Mamoru's past incarnation. They were suspicious of the Moon and its constant surveillance of the Earth, and were shown arguing with Endymion about this. It was implied that this suspicion was what caused them to turn to Beryl. Despite this, they were shown to be shocked by Prince Endymion's death. In the manga, the Shitennou were still rivals, but they also cared a lot about each other, and were upset by each others' deaths. There was an element of vengeance in both Nephrite and Zoisite's attacks for what happened to Jadeite (and later Nephrite).
After their deaths in the present, each was laid out in state. When the Silver Crystal appeared, the three that were already dead returned briefly to life and Kunzite's memories of the past returned. However, his three dead comrades then dissolved and became the stones of their names. After Kunzite was killed, this happened to him as well. The possessed Mamoru picked these stones up and puts them in his chest pocket, and the stones stopped him from being killed when Sailor Moon stabbed him. The spirits of the Shitennou appeared to Mamoru and told him how Metalia could be killed, told him to be happy, and then disappeared. Mamoru later kept the stones in a special box and called on them from time to time throughout the manga, most especially during the Dream arc, when he came into his powers as the holder of the Golden Crystal, the Earth's Sailor Crystal.
Of the picture of each Shitennou paired up with a Senshi Naoko Takeuchi wrote, "This is the title page for the conclusion of the first series of Sailor Moon. It had a great deal of impact on the first series. Probably because the four couplings on the right side were very unexpected. I was thinking of love stories of the previous lives of these couples. I'd like to be able to draw that someday..."
Despite this, only Kunzite and Sailor Venus were shown to have had any kind of relationship, both in the Sailor Moon and the Codename: Sailor V manga. Jadeite was attracted to Rei in the manga, and he was shown in a side story concerning her, but this was not followed through. There was no evidence of a relationship between Zoisite and Sailor Mercury or Nephrite and Sailor Jupiter.
The subject of a romance between the two sets of guardians, and whether it should be counted as canon or not, has long been debated in the fandom. Those that count it as canon argue that because Naoko Takeuchi is the creator of the Sailor Moon universe, her words above show that in her mind the romance between the eight took place. Thus, it is canon. The common argument against this is simple - it never took place in the anime or manga and therefore is not canon.
 Pretty Guardian Sailor Moon
The live-action series combined the anime and manga: the Shitennou were still Mamoru's guardians, and were also evil and vying for Queen Beryl's attention. They could also come back after being killed, unlike in the other two continuities, so the relationships lasted longer and were more complicated. They were also closer to being human, with Nephrite being turned into one and Kunzite being turned from one. Their personalities were developed and their memories of the past life were much closer to the surface, which resulted in more tension with Mamoru. This was especially apparent with Kunzite, who blamed his master for what happened to the planet Earth.
Little was stated in canon about the Shitennou's fates after the Final Act, but they did return to help Mamoru once more in the fight with Mio Kuroki in the Special Act. They also appeared at Usagi and Mamoru's wedding, although whether they were apparitions or physically present was unclear.
There was no romance with the Sailor Senshi in the live-action series, although there seemed to be some sort of connection between Nephrite and Sailor Mercury. After becoming human, he bought a gift for her, though it appeared he never got the chance to give it to her. More remotely, Kunzite seemed to have shown some affection towards Dark Mercury, the evil form of Sailor Mercury, though it was not reciprocated. Zoisite and Sailor Venus also forged a sort of alliance due to their similar goals.
The Shitennou appeared in several of the musicals, with slightly different roles in each. In Sailor Moon - Gaiden Dark Kingdom Fukkatsu Hen, the Shitennou were romantically paired with the Inner Senshi, making the musicals the only version of the series in which those relationships were canon. In Starlights - Ryuusei Densetsu, they appeared again disguised as the "Jewel Metalias."
The musical Kakyuu-Ouhi Kourin introduced a group that called itself the "Neo Shitennou," and included three members who were not in the original group. The members of the Neo Shitennou were Kunzite, Hematite, Hiddenite, and Kalunite. No explanation was given for why they had different names, although Hematite, Hiddenite, and Kalunite strongly resembled Zoisite, Nephrite, and Jadeite, respectively. They worked with the reborn Queen Beryl under Sailor Galaxia, though the five of them were simultaneously plotting ways to get out from under the powerful Senshi's rule. As part of their plans, they had civilian guises as the "Jewel Managers."
- In the anime, three of the four Shitennou discovered Sailor Moon's civilian identity shortly before their deaths:
- Jadeite discovered the identities of Sailor Moon, Sailor Mercury, and Sailor Mars in episode 13, the same episode in which he died.
- Nephrite discovered the identity of Sailor Moon in episode 24, the same episode in which he died.
- Zoisite discovered the identities of Sailor Moon and Tuxedo Mask in episode 34, then died in episode 35.