This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
Lieutenant Commander Paul Stamets was a male Human astromycologist and Starfleet officer who lived during the mid-23rd century. He became part of the team that discovered the mycelial network and helped develop the experimental spore drive propulsion system. In that capacity he served as the spore drive specialist of the USS Discovery in 2256, traveling the network hundreds of times. (DIS: "Context Is for Kings", "Choose Your Pain", "Project Daedalus")
As the Discovery's spore drive specialist, he was the first to make the spore drive viable for traversing great distances by using himself as an organic navigation computer, making the ship an invaluable asset in the 2256-57 war with the Klingon Empire. His frequent exposures to the mycelial plane led him to exist partially outside the universe's normal flow of time. This caused progressive neurological damage to Stamets' body, and when Captain Gabriel Lorca deliberately sabotaged a spore drive jump to take the Discovery into the mirror universe, Stamets was left almost catatonic. His consciousness survived inside the mycelial network, however, and he was restored to health by Cadet Sylvia Tilly. Using his knowledge of the network, he was able to devise a plan to return to the prime universe by destroying the super-mycelial reactor of the Terran Empire flagship ISS Charon. (DIS: "Magic to Make the Sanest Man Go Mad", "Into the Forest I Go", "Despite Yourself", "What's Past Is Prologue")
Upon the Discovery's return to the prime universe in mid-2257, Stamets' control of the spore drive was instrumental in allowing the vessel to conduct a mission to Qo'noS to force an armistice in the Federation-Klingon war. For his role in the conflict, Stamets was awarded the Starfleet Medal of Honor and promoted to the rank of lieutenant commander. (DIS: "The War Without, The War Within", "Will You Take My Hand?")
Stamets trained as an astromycologist. Prior to the outbreak of the Federation-Klingon War in 2256, Stamets and his research partner, Straal, were working on an experimental propulsion technology known as the spore drive. This made use of prototaxites stellaviatori spores linked to the so-called mycelial network and could theoretically allow a starship to travel great distances instantaneously. Stamets and Straal worked on the project together for nearly twelve years, but failed to achieve decisive results. When the war started, Stamets and Straal were co-opted by Starfleet to develop military applications for the technology. Stamets and Straal were assigned to the Crossfield-class starships USS Discovery and USS Glenn respectively, experimental vessels that were the first to be built around spore drive technology. (DIS: "Context Is for Kings")
While aboard the Discovery, Stamets shared quarters with his husband, Lieutenant Commander Doctor Hugh Culber. He was uncomfortable with his work being co-opted for military purposes, and regarded his commanding officer, Captain Gabriel Lorca, as a warmonger. Despite six months of research, by late 2256 both the Discovery and the Glenn were still unable to make spore drive jumps greater than intervals of Speirin 12 for the former (a few hundred kilometers) and Speirein 240 for the latter. Stamets remained in regular correspondence with Straal, who by the end of the year was ready to consider a spore drive jump of Speirein 900, which Stamets felt was unsafe. (DIS: "Context Is for Kings")
At this time, Stamets met Michael Burnham after her disabled prison shuttle was rescued by the Discovery at Captain Lorca's direction. Despite being a convicted mutineer, Lorca assigned Burnham to work under Stamets in the hopes that her predictive mind and determination would help him make the spore drive viable. Initially affronted by this, Stamets was soon forced to confront other issues when a distress call was received from the USS Glenn. Stamets and Burnham were part of the team sent aboard to investigate, and discovered that the ship was a derelict with the entire crew having been severely mutilated, including Straal. Stamets deduced that the Glenn had been destroyed by an accident with its spore drive, and the team was soon ambushed by an immense creature. With the aid of Burnham, the creature was captured and brought aboard the Discovery. (DIS: "Context Is for Kings")
The creature was dubbed a "tardigrade" for its resemblance to the microscopic Earth creature. Soon nicknamed "Ripper" for its apparent aggression, Stamets soon realized that it was able to communicate with the mycelial network and that the Glenn had used it to improve its spore drive. Though initially reluctant to attempt the same process, Stamets was convinced by Lorca's appeal to his sense of scientific wonder. Linking the tardigrade into the spore drive while exposing it to prototaxites stellaviatori in the spore chamber transformed the creature into an organic navigation computer, and allowed the Discovery to make a long jump to halt a Klingon attack on the mining colony of Corvan II. (DIS: "Context Is for Kings", "The Butcher's Knife Cares Not for the Lamb's Cry")
Stamets had made the spore drive viable. Intensified development of the spore drive began on Earth while all Federation ships, starbases, and colonies were placed on alert to search for more tardigrades. However, forcing Ripper to act as a navigation computer caused it immense pain and it soon became obvious that each jump was severely debilitating to it. After Captain Lorca was taken prisoner by the Klingon Empire, repeated use of the spore drive in attempts to rescue him resulted in Ripper entering an extreme state of cryptobiosis and becoming unresponsive. It was subsequently released by Michael Burnham. (DIS: "Choose Your Pain")
Stamets was under pressure from the first officer, Commander Saru, to restore the spore drive. With the help of Cadet Sylvia Tilly, Stamets resorted to injecting himself with a sample of tardigrade DNA and entering the spore chamber to act as the navigation computer. The jump was a success and Lorca was recovered, along with another Starfleet prisoner, Lieutenant Ash Tyler. The exertion of the jump briefly knocked Stamets unconscious, but he recovered with apparently no ill effects. (DIS: "Choose Your Pain")
Events soon proved that Stamets' exposures to the mycelial network were changing him fundamentally: due to his mixing of tardigrade DNA during his usage of the spore drive, his consciousness came to exist outside the universe's normal flow of time. He began seeing flashes of what were later discovered to be events in the mirror universe, including images of his counterpart, and once briefly mistook Cadet Tilly as hers. His crewmates, however, only noticed that his scientific success had caused more positive sides of his personality to emerge. His partial displacement in time meant that he was the only crewmember to notice when the Discovery was trapped in a repeating thirty-minute time loop created by the con man Harcourt Fenton Mudd. Mudd used the loop, generated with a time crystal, in an attempt to steal the Discovery and sell it to the Klingons; however he was unable to account for Stamets, who was able to alert the crew and foil Mudd's plan. (DIS: "Choose Your Pain", "Lethe", "Magic to Make the Sanest Man Go Mad")
To improve his connection to the spore drive, Stamets accepted cyborg augmentations to his arms. However, he was increasingly aware that use of the spore drive was taking its toll on his mind. He confided only in Cadet Tilly, refusing to tell Dr. Culber out of fear it would place his partner in emotional conflict over whether to alert the rest of Starfleet to his condition. (DIS: "Si Vis Pacem, Para Bellum")
While investigating the planet Pahvo, Captain Lorca saw an opportunity to destroy the Klingon starship Sarcophagus and develop a way to penetrate cloaking devices. To accomplish this Stamets would have to conduct 133 micro-jumps with the spore drive so the Discovery could gather data from multiple angles to generate the algorithm to penetrate the cloak. In the subsequent battle at Pahvo, the Discovery succeeded in destroying the Sarcophagus, killing the Klingon leader Kol and capturing L'Rell, who was believed to have tortured Ash Tyler while he was a prisoner. However, Stamets was visibly distressed from the effort of conducting so many jumps in such a short time, and declared to Lorca that he would conduct one last jump to get the Discovery to Starbase 88 before submitting himself to Starfleet Medical for evaluation. However, the man who the Discovery crew believed to be Captain Gabriel Lorca was in fact his mirror universe counterpart. This Lorca deliberately sabotaged the jump, using a theoretical application of the spore drive to take the Discovery into the mirror universe. The effect of this plunged Stamets into near-catatonia: his eyes became a blank white and when he spoke it appeared incoherent and delirious. Without Stamets, the Discovery had little chance of returning to the prime universe. (DIS: "Into the Forest I Go")
Trapped in the mycelial network
Stamets' consciousness was in fact trapped in the mycelial network. Through that he still had some contact with the physical world, violently blurting out "Don't go to palace!", and whispering "The enemy is here" in brief moments of lucidity. Dr. Culber saw this as insane rambling. However, while Stamets was still unconscious, Culber was murdered by the increasingly-unstable Lieutenant Ash Tyler. It was subsequently discovered that "Ash Tyler" was in fact the Klingon Voq, physically – and mentally – transformed into the real Tyler's form to act as a spy, and Voq's personality had been partially-awoken by the presence of L'Rell. Stamets remained aware of this though his mind remained disconnected from his body, and he was discovered in one of Discovery's corridors cradling Culber's corpse (DIS: "Despite Yourself", "The Wolf Inside")
Cadet Tilly compared Stamets' brain scans to those of the tardigrade, and discovered that Stamets' brain had developed a similar makeup. Since the tardigrade had been cured before its release by exposure to the mycelial spores, Tilly reasoned that a similar treatment might improve Stamets' condition. Under such treatment, Stamets' physical signs improved across all biological metrics, though mentally he remained in the mycelial network. There he encountered his mirror counterpart, who had been working on similar experiments. Together they explored the "USS Stamets", an illusory starship created by the network from Stamets' memories, attempting to find a way out. They encountered a spreading corruption within the network, and fled into the "main engineering" of the illusion. (DIS: "Vaulting Ambition")
After the war
After the war has ended, Stamets considered taking a permanent job at the Vulcan Science Academy, but eventually decided to stay on board the Discovery, temporarily under the command of Captain Christopher Pike. (DIS: "Brother")
Teamed up with Jett Reno, Stamets helped removing a multidimensional fungus creature known as jahSepp from Ensign Sylvia Tilly, when the creature infected her, posing as "May Ahearn" in Tilly's mind. (DIS: "Point of Light", "An Obol for Charon")
When the creature abducted Tilly into the mycelial network, Stamets navigated the Discovery itself into the network, and, along with Michael Burnham, volunteered to venture into the network, in search for the missing Ensign. Stamets found his partner, Hugh Culber, previously presumed dead, inside the network, and succeeded in rescuing him, removing the "Monster" which "infected" the jahSepp's living environment. (DIS: "Saints of Imperfection")
Stamets was among the Discovery crewmembers, who volunteered to stay on board and accompany the ship and Michael Burnham into the far future, with no chance of return. Stamets was injured during the battle near Xahea, and was in a comatose state, treated in sickbay when the Discovery crossed into the 32nd century. Afterwards, he was presumed dead by Starfleet, based on the testimonies of the USS Enterprise senior officers. (DIS: "Such Sweet Sorrow", "Such Sweet Sorrow, Part 2").
In 3189, Adira Tal developed a method for Stamets to have his cybernetic enhancements removed due to a new Spore Hub Control mechanism she developed. Stamets later admitted after their removal that he always hated them. (DIS: "Scavengers").
Stamets was in a relationship with Doctor Hugh Culber. The two first met in a cafe on Alpha Centauri. (DIS: "Choose Your Pain", "Magic to Make the Sanest Man Go Mad") Michael Burnham described him as a widower shortly before Hugh was resurrected from the mycelial network. (DIS: "Saints of Imperfection")
Stamets had at least one sibling, who he considered his best friend. He also had a mom and a dad, and an uncle named Everett who sang in a Beatles cover band. (DIS: "Such Sweet Sorrow", "Context Is for Kings")
Over the course of Sylvia Tilly's assignment to Discovery, the two grew to be close friends and colleagues. When he was offered a position at the Vulcan Science Academy, Tilly was among the first to ask him to reconsider. (DIS: "Brother")
Paul Stamets was played by Anthony Rapp.
This character was named for real-life mycologist Paul Stamets, who was the inspiration for the science of Discovery. However, much of the character was based on Executive Producer/Writer Aaron Harberts, who commented, "Stamets is kind of cranked up. But when writing Stamets, there was a lot of 'What would I say here? Probably that.'" (AT: "Context Is for Kings")
Stamets, along with his partner Culber, are the first openly gay regular characters in a Star Trek television series. Prior to the Discovery premiere, original showrunner Bryan Fuller commented, "Star Trek started with a wonderful expression of diversity in its cast… we're continuing that tradition."  In "The Red Angel", Stamets became the first Star Trek character to specifically refer to himself as gay (also so describing Culber).
A graphic seen in "Choose Your Pain" referred to Stamets as the chief engineer, but Ted Sullivan discarded this as a production mistake, quipping, "I'd say he's the chief engineer of spore drive but not of engineering." 
Stamets appears in the "Awakening" expansion to Star Trek Online, with Anthony Rapp voicing him. In the mission "Beneath the Skin", the renegade Klingon matriarch J'Ula unleashes a mycelium-based weapon at Andoria, which tears open a rift that leads to the mycelial network. As astromycology is a largely forgotten science by 2410, and most of what is known is classified by order of Starfleet Command (following the "destruction" of the Discovery in "Such Sweet Sorrow, Part 2"), Captain Sh'marois of the USS Hoffman creates a holographic Stamets, his memory based on the real Stamets' Starfleet record and research notes. The holographic Stamets is equipped with a mobile emitter and accompanies the player character and their away team into the mycelial network, where they encounter a jahSepp in the form of deceased USS Buran security chief Amna Patel, asking for help in repairing the damage done by J'Ula. The holo-Stamets is granted memories from the real Stamets that remained from his time in the network, allowing him to better guide the player captain.