(covers information from several alternate timelines)
This page contains information regarding Star Trek: Picard, and thus may contain spoilers.
The Son'a were an interstellar power, originating from Ba'ku, from which they were exiled in the late-23rd century. They were nomadic, though they maintained outposts. Their command structure was called Son'a Command.
Son'a were considered a narcissistic and materialistic people. They put great value in precious metals, rare jewels, and other materials, the desire for which was thought antiquated by Federation standards. They raided inhabited worlds in search for these resources, and also for slave labor, especially females. However, by 2375 it was believed that this practice had ended.
Without the regenerative effects of the Ba'ku homeworld's metaphasic radiation, the Son'a became desperate in their efforts to prolong their lives by any possible means, including genetic manipulation and surgical techniques. The Son'a would make regular visits to facilities where their skin was stretched tight, and accumulated toxins were purged from their bodies. Nevertheless, due to the amount of bacteria entering their system, in the 2370s many Son'a (including Ru'afo himself) were suffering from fatal diseases and nearing death. It was also revealed that it would take at least ten years of normal exposure to the metaphasic radiation to begin to reverse their condition.
Some sociologists attributed their aggressive behavior to desperation brought on by their infertility. On a more positive note, the Son'a were highly praised for their accomplishments in the arts, the high quality of their vinting and their "hospitable" attitude towards personal relationships.
While a race of hedonists, they were well educated and curious, possessed of a strong desire to know all they did not, as befitting of the younger generation of Ba'ku, indeed, it was the very reason they had set out in the first place, this had led to many scientific advancements, including study of the metaphasic particles of their former homeworld.
The Son'a were originally Ba'ku, living on the idyllic Ba'ku home planet in the Briar Patch. In the late 23rd century a group of young Ba'ku desired to follow the way of the offlanders. They attempted to take over the Ba'ku planet, but failed and were exiled.
After a brief flirtation with space colonization, this group settled into a pattern of nomadic acquisition. They would raid planets for resources and slave labor, and about half a century before 2375 subjugated the Tarlac and Ellora species to serve as indentured servants and soldiers. The Federation sanctioned them multiple times, and by the 2370s the slave raiding was thought to have stopped as a result.
By the 2370s, Son'a maintained colonies in the outlying areas near Cardassia and the Bajoran wormhole. By this time the Son'a had become infertile as well. The Federation speculated that this might have been the result of biological or genetic engineering. (Star Trek: Insurrection)
In 2375, a group of Son'a led by Ahdar Ru'afo attempted to access the metaphasic particles within the rings of the Ba'ku planet, now located within Federation space. To do so, they entered an alliance with Starfleet Admiral Dougherty, who convinced the Federation Council to approve the scheme. The Son'a had developed a metaphasic collector to harvest the particles, but it came with the secondary effect of rendering the planet uninhabitable. They agreed to follow Starfleet procedure and relocate the existing Ba'ku population beforehand, using a hidden Federation holoship.
The plan began to unravel when Lieutenant Commander Data from the USS Enterprise-E uncovered the holo-ship and was shot by a Son'a soldier. This caused him to malfunction and the Enterprise was sent to retrieve him. When the Enterprise arrived, they discovered the true nature of the Son'a's operations, the crew rejecting Dougherty's claims that the relocation of the small number of Ba'ku on the planet was worth it compared to the billions who would be helped by the subsequent advances in medical technology as they felt that the moral cost that would be paid in the destruction of the Ba'ku culture was too great. Captain Jean-Luc Picard threatened to expose this to the Federation, by sending Commander William T. Riker and the Enterprise to the edge of the Briar Patch to contact the Federation Council, while he and a number of his officers took the captain's yacht to the surface to help the Ba'ku. In response, Ru'afo sent Son'a warships to intercept the Enterprise and ordered the Ba'ku to be removed by force, though his efforts were impeded by the Enterprise crew.
Unwilling to wait any longer, Ru'afo decided to commence with the next stage of the operation, without relocating the remaining Ba'ku. When Dougherty objected to this, Ru'afo killed him and deployed the metaphasic collector. Fortunately, Picard was able to stop its activation and trigger the auto-destruct sequence, with help from Ru'afo's second-in-command Gallatin. Soon the Federation Council withdrew their support for the project, with new information from the Enterprise. Some of the Son'a elected to return to the Ba'ku. (Star Trek: Insurrection)
During the Dominion War, the Federation suspected that they were manufacturing large quantities of the Dominion narcotic ketracel-white in the Son'a colonies in the outlying areas near Cardassia and the Bajoran wormhole. In the later days of the war, a recently constructed facility indeed existed at their Devos II outpost. Weyoun diverted a number of Dominion warships to that colony, believing that the Federation knew about it. Damar questioned this, as he felt the Son'a should be able to protect it themselves. (Star Trek: Insurrection, DS9: "Penumbra")
In an alternate timeline created by Q, the Son'a founded the Son'a Empire. This empire was speculated by the Confederation of Earth to have provided disruptor rifles to the Zhat Vash after the fall of Romulus in the late 24th century. (PIC: "Penance")
The Son'a had developed technologies that surpassed that of the Federation. They had developed the technology to harness the metaphasic radiation from the Ba'ku planetary rings, something that some of the brightest minds of the Federation had not achieved. According to Dougherty's words, this was the main reason why the Son'a and the Federation entered in this "partnership".
The Son'a equipped their vessels with photon torpedoes and unpredictable isolytic subspace weapons, in defiance of the Second Khitomer Accord. The Son'a used hand-held disruptor weapons that fired plasma charges. (Star Trek: Insurrection)
A lot of the information in this article, particularly about the Son'a's early history and culture, was not stated on-screen but instead derives from their file, as studied by Riker and Troi while the Enterprise-E was underway to the Briar Patch.
In the development of Star Trek Insurrection, the Son'a replaced the Romulans in the story; because the film's creative staff lacked interest in the Romulans, the Son'a were instead invented. (AOL chat, 1997)
Among the items sold off on the It's A Wrap! sale and auction on eBay was an unused special effects Son'a face make-up mask. 
According to the Star Trek: Star Charts:
- Page 55: The Son'a's homeworld was Son'a Prime. This was a class K planet governed by the Son'a Solidarity from their capital city Son'a. Son'a Prime was settled circa 2275.
- Page 56: Son'a Prime was located in the Son'a star system. This system's primary was a red giant.
When it came time to design the Son'a ships, Illustrator John Eaves took inspiration from everyday objects that caught his eye. "All the Son'a ships are from activity games I found out in the backyard," he said. "I wanted to give a whole different kind of look to their architecture, so I kind of went with yard toys – Ru'afo's ship is based on a horseshoe, the battleship is based on a boomerang, the shuttle is a yard dart, and the science vessel ... well, the front of it is sort of a badminton shuttlecock turned inside out." (Star Trek: The Magazine Volume 1, Issue 3, p. 21) In fact, Eaves incorporated the horseshoe motif into the designs for several of the Son'a vessels rather than just Ru'afo's craft, later stating, "The Son'a ship designs are kind of based on a horseshoe." (The Secrets of Star Trek: Insurrection, p. 87)
John Eaves elaborated on his initial ideas for the Son'a ships by adding details he got elsewhere. "[The ships] also have a kind of an inset detail that looks like a bunch of riblets; I based that on the strings inside a piano. I thought it would be fun to do that – their design is kind of like intricate wiring and framework, which is inset but open so you can see it. That was what I used as their kind of icon of design. It's on all the ships to an extent; you can see it extensively on Ru'afo's ship and the battleship, while the other had it inserted." (Star Trek: The Magazine Volume 1, Issue 3, p. 21) The Grand Piano concept for the internals was inspired during Eaves' visit to a soundstage while Jerry Goldsmith scored Star Trek: First Contact there. "The big grand piano was open, and I remember seeing all those strings. And I thought, 'Wouldn't be that a great idea for a ship?' And when Insurrection came along, I thought, I transfer all those ideas over. And so everything you'll see in the Son'a world has kind of an open piano look. You see a lot of repetitive strings, a lot of repetitive kind of wiring going through the main architecture." ("The Art of Insurrection", Star Trek: Insurrection (Special Edition) DVD)
The Son'a ships were constructed in CGI by Santa Barbara Studios. SBS' Effects Supervisor John Grower stated, "John [Eaves] sent us elevation views and one or two 3/4 perspective drawings of each ship, but we had to do a lot of deduction work. The Son'a Flagship and Battleships had very complex shapes and all of these incredible compound curves, which didn't appear in the plan views. They're thin in one dimension and very wide and long in the other, kind of like a trilobite. The biggest challenge was that the Son'a ships didn't look the same from one angle to the next, so if we rotated around them a little bit, their profile changed because they had hundreds of compound curves that hooked together to form their shape. Getting it all to flow involved a ton of work and a very long modeling process." (American Cinematographer, January 1999, pp. 41-42) Though the Son'a were later mentioned in the Star Trek: Deep Space Nine television series episode "Penumbra", their ships were never again featured, so the CGI models were not upgraded in the LightWave 3D CGI software.