The Vidiians were a species found in the Delta Quadrant. For two millennia, the entire race suffered from a disease called the Phage that ate skin and internal organs, and damaged their DNA. They were considered with the Borg and Species 8472 as the prime examples of hostile species encourtered by Voyager in Delta Quadrant. (VOY: "Good Shepherd")
The Vidiians were once a race of educators and explorers, renowned for their artistic achievements, until the Phage attacked approximately 2,000 years ago. Their civilization was ravaged and they turned all their attention to treating the disease.
By the 24th century, they had been forced to use their technology to harvest other species' organs to replace their own as they failed. Defeating the Phage became an obsession, and many of their politicians and scientists lost perspective, failing to consider other beings. As a result, forcibly removing organs from live subjects as necessary occurred, although some exceptions objected to these practices and were prepared to help others. A profession called a Honatta had even developed that was dedicated to harvesting organs and biomatter from others, typically from corpses, for those suffering from the Phage. (VOY: "Phage", "Lifesigns")
The first Starfleet encounter with the Vidiians occurred in 2371 when the USS Voyager visited an asteroid used by the Vidiians as an organ storage facility. A Talaxian crewmember, Neelix, had his lungs removed and implanted into one of the two Vidiians on the asteroid. Consequently, Captain Janeway was faced with killing the Vidiian to recover the organs. Feeling that this would be morally wrong, and recognizing her lack of options this far from Federation space, she agreed to release them with a warning to their species not to interfere with Voyager again. As thanks for the captain's decision to spare them, the Vidiians agreed to use their advanced medical technology to transplant a lung from an Ocampan crewmember, Kes, into Neelix. (VOY: "Phage")
Later that year, B'Elanna Torres was captured by Sulan, the chief surgeon of the Vidiians, and separated into her Human and Klingon halves. The Klingon half proved resistant to the Phage but was killed as the other captive Starfleet personnel escaped from the Avery III mines. (VOY: "Faces")
Another encounter occurred due to a temporal incursion. In this encounter, a future version of Kes, driven mad by her enhanced powers, became convinced that Voyager had corrupted her with ideas of exploration, prompting her to develop her mental powers to such an extent that her people would be afraid of her, and became determined to change her history. Once in the past, she contacted a Vidiian ship, and agreed to give them Voyager if they would take her past self home. However, Janeway realized what was happening and confronted the future Kes, killing her as Voyager escaped the Vidiian ship. This encounter allowed Janeway to learn about the future, allowing her to create an alternate future where the older Kes returned to Ocampa instead of time traveling. (VOY: "Fury")
The species was encountered three times during 2372. In the first instance, Voyager rescued Danara Pel, a dying Vidiian hematologist. Her condition was stabilized by The Doctor and she proved to be the first Vidiian Voyager met who explicitly disapproved of the practice of organ harvesting, even assuring Torres that she didn't want her to go through an operation that would help Pel if she didn't want to. Pel and The Doctor developed a relationship (the first time The Doctor had ever developed romantic feelings), but she left Voyager to help her people, although they both treasured the time they spent together. (VOY: "Lifesigns")
The second encounter was less positive. After passing through a subspace anomaly, Voyager was mysteriously duplicated. One of the two duplicates was attacked by a Vidiian vessel and invaded by hundreds of Vidiians. With numerous crewmembers such as Tuvok now dead, the Captain Janeway of that ship destroyed Voyager rather than let it fall into enemy hands. As a result, almost the entire crew of that Voyager was killed, with the exception of Harry Kim and the newly-born Naomi Wildman, who were ordered to escape to the surviving duplicate Voyager (their counterparts having died due to a hull breach and birth complications, respectively). During this attack, the Viidians appeared to be able to identify presumed foreign species, such as Vulcans. (VOY: "Deadlock")
Several months later, Captain Janeway and Chakotay were bitten by an insect while exploring a planet and were infected by a virus. The Doctor was unable to find a cure and only exposure to the planet's ecosystem held the symptoms at bay. With no other option, Voyager continued its journey, leaving the two officers behind.
Some weeks later, Voyager encountered a Vidiian convoy. After initially avoiding contact, Tuvok decided to ask them about the virus. Shortly afterwards they were contacted by Danara Pel, who agreed to give them the anti-viral agent that the Vidiians had developed many years before.
Upon meeting the convoy, the Vidiians attacked, but Danara Pel, shocked at her own species' actions, offered to transport the anti-viral agent anyway, talking briefly with The Doctor one last time before they parted ways forever. Voyager then disabled the Vidiian ships and returned to pick up Janeway and Chakotay. (VOY: "Resolutions")
By 2375, the Think Tank claimed to have successfully cured the Phage. In doing so, the Think Tank also stated that "you wouldn't recognize them now," insinuating that they had returned to their pre-Phage pursuits, ideals, and morals. (VOY: "Think Tank")
Continuous organ transplantation led to the Phage-infected Vidiians having a wide variety of alien organs and skin on their body, resulting in a hideous appearance. When uninfected with the Phage, the Vidiians had a standard humanoid appearance. The Vidiians' facial appearance was similar to that of a Human with two eyes, a nose and a mouth, but they also possessed a swept back hairline and a slightly enlarged forehead with no eyebrows. There was also a slight ridge that ran from the hairline down the center of the forehead to the top of the nose.
Vidiians had a very sophisticated device that was a combination of a weapon, medical scanner, and surgical instrument. With this device, Vidiian organ harvesters would attack a victim who the device indicated had healthy and Vidiian-compatible organs or tissues, and transport such bio-material from the victim into the transporter device used. The organs were then transplanted into another Vidiian requiring organ transplants. (VOY: "Phage")
Vidiians also had force field technologies, including the ability to cloak the force field as an object, like a rock face. They had an advanced medical technology, superior to even that of the Federation, but this was not enough to cure the Phage. Their anti-starship weaponry included hyper-thermic charges. Despite the use of similiar tech in their organ-harvesting devices, Vidiians lacked personnel transporter technology and relied on docking equipment to capture alien vessels. (VOY: "Deadlock")
Society and culture
By the 24th century, much of the Vidiian culture was shaped by their health needs. Congregating in groups was strictly regulated, as it was considered to be a threat to public health. Healthy Vidiians would shun sick ones, even if they had previously been friends. They seemed to be unfamiliar with the concept of dancing. (VOY: "Lifesigns")
The Vidiians were originally supposed to be called the Vaphorans, but their name was changed because the original was considered too difficult to pronounce. "Phage", the episode that introduced the species, was shot using the original name, and the new name was looped in post-production. 
The makeup department designed the Vidiian makeup as if they were patchwork quilts, built out of harvested organs and body parts to replace those that were consumed by the Phage. To make the Vidiians walking mosaics of the creatures whose skin they grafted on, the department used the skin designs from previous aliens, patches of Talaxian spots here or an orange Kazon patch there, so as to reinforce the image of the Vidiians as bioscavengers of the Delta Quadrant. (Star Trek: Aliens & Artifacts, p. 167)
Several Vidiian production items were later sold off in the It's A Wrap! sale and auction, among them a complete Vidiian headpiece (sold for US$355.00), Vidiian hand molds (sold for US$86.85) and a collection of Vidiian rubber makeup applications (sold for US$26.00).        
The reference book Star Trek: Star Charts (p. 78) gives the name of the Vidiian homeworld as Vidiia Prime, the main planet in the Vidiia system and a Class M world. On page 83, it is said that first contact with the Vidiians occurred on stardate 48532.
Additionally, Star Trek: The Visual Dictionary (p. 93) describes the Vidiians as a proud race known for their arts and culture.
The Star Trek: Myriad Universes short story "Places of Exile" describes an alternate timeline whereby the Phage is cured thanks to the combined efforts of The Doctor and Danara Pel. While it would take a long time for them to repair their civilization, the grateful Vidiians nevertheless offer the Voyager crew protection if they ever return to their part of space.
In the Star Trek Online mission "Dust to Dust," the Harry Kim killed in "Deadlock", having been revived by the Kobali, accuses them of working with the Vidiians as he had never met them before his untimely death.