(covers information from several alternate timelines)
The Crossfield class was a type of Federation starship in service during the mid-23rd century. Though officially designated as a science vessel, during the Klingon-Federation War the class was re-classified as a warship. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")
Two ships of the class were equipped with an experimental spore drive propulsion system, the USS Discovery and its more advanced sister ship, the USS Glenn. In November of 2256, "Stone" and "Psycho" noted that Discovery appeared to be a brand new starship, without even "a scratch on the floor" of the shuttlebay. Both the Discovery and the Glenn had been commissioned by that time. (DIS: "Context Is for Kings")
To facilitate the operation of the spore drive, the saucer section was divided into three concentric sections separated by gaps. When engaging the spore drive, the ship went into black alert, which alerted the crew to the drive's activation. The outer and middle sections housed rings that could rotate clockwise and counter-clockwise respectively, so as to provide excess energy cavitation. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry")
32nd century refit
During the late 3180s, the Crossfield-class underwent an extensive retrofit. The process took around three weeks to complete and the overall layout was near-identical to before consisting of a saucer section, a wide secondary hull, and two elongated nacelles. However, there were several alterations both aesthetic and design wise. For example, the hull was no longer copper colored and instead was chrome. More major changes were the complete removal of the connecting corridors between the outer ring and inner ring as well as the formerly round deflector dish were given an overhaul as it now appeared hexagonal.
The nacelles were now physically detached but remained connected to the vessel through magnetic seals using superconductors which enabled an improved level of maneuverability during flight. While the warp drive or spore drive was active, the nacelles resumed their former position without detachment. Additionally, the secondary hull appears to have been gutted and changed to accommodate newer impulse engines, with a different shape; the neck of the ship was thinner with a more V-shaped appearance from the rear view, fewer windows, and was generally sleeker.
The turboshafts were entirely removed and were now free floating inside the ship with the magnetic levitation tracks being constructed as the turbolifts moved, thanks to programmable matter. (DIS: "That Hope Is You, Part 2")
Crossfield-class starships were equipped with at least six tractor beam emitters for towing objects in space, two on the ventral engineering hull (port and starboard), two above the aft doors to the cargo bay to guide boarding shuttles, and two dorsal on the inner ring of the saucer section. (DIS: "Context Is for Kings"; ST: "Calypso")
32nd century refit tactical systems
Following the retrofit, Crossfield-class vessels acquired a standard Federation cloaking device like many ships in the era, allowing ships of this class to cloak. The act of cloaking was accompanied by a green alert. In 3189, the spore drive could not function while cloaked but this problem was rectified by the following year.
The armaments did not change much, still consisting of deflector shields, photon torpedoes, and phasers, albeit they were all upgraded to be on par with 32nd century weaponry. For example, the phasers no longer fired blue beams but rather green using an unknown particle composition and the shields were now reinforced enough to hold out against an entire fleet of starships firing on it in comparison to previously failing after a single quantum torpedo detonation. Programmable antimatter was used to fortify the shields in anticipation for crossing the galactic barrier. (DIS: "The Galactic Barrier")
Two vessels of this class were known to be utilized by Starfleet to test a theoretical spore drive, following the outbreak of war with the Klingons in 2256. Shortly after achieving a breakthrough, the USS Glenn was crippled and all crew killed in an accident. She was then scuttled by her sister ship, the USS Discovery. (DIS: "Context Is for Kings")
Ships of this class also included a regular warp drive for faster-than-light propulsion.
32nd century refit
As part of the ship's refit, Adira Tal also included an upgrade to the spore drive reaction cube as well as converting the physical injector shunts into nanogel control interfaces which acted as a quantum transducer. The impulse engines were updated to conform to 32nd century standards and the warp core was completely replaced, technically twice as the originally overhauled warp core was ejected and subsequently exploded.
After the refit, the Crossfield-class no longer utilized duotronic circuitry within its computational systems. Instead, it favored angular isolinear chips within the main computer core. In addition to all current Federation databases of the 32nd century, the ship had access to data lost or damaged during The Burn as well as a hundred thousand years of observations experienced by the Sphere, including statistical measurements of Kaminar, artificial intelligence, Trill, and Trill symbionts.
The merger of the Sphere and the Discovery initiated a natural evolution of the ship's computer, which was accelerated by the integration of 32nd century technology resulting in Zora. Zora was a fully sentient AI with emotions and unlimited access to all of the ship's systems including her own programming, meaning she had autonomous operation of her existence and could prevent herself from being removed in addition to altering her core parameters. (DIS: "...But to Connect")
The ships' design featured polygonal windows to space in crew support compartments including the mess hall and crew quarters. Those same rooms, as well as sickbay and the corridors, mirrored the window design through recessed alcoves on the wall. (DIS: "Context Is for Kings")
Main bridge and command deck
The main bridge was located on deck one, with a central command chair for the commanding officer, turbolift access at the front-starboard and rear-center, and a computerized transparent window-viewscreen. Clockwise from the center command chair, the bridge stations comprised of a free-standing multi-purpose station, science, another free-standing multi-purpose station, tactical, helm, operations, spore drive control, communications, and a free-standing science station. (DIS: "Context Is for Kings", "Brother")
In 2257, Captain Christopher Pike favored a ready room disconnected from the bridge. This ready room featured a more personalized décor, additional seating, and a conference table as well as a food synthesizer slot and several computer panels. (DIS: "New Eden")
Paul Stamets and his Glenn counterpart Straal operated their spore drives from engineering test bay alpha, a standard engineering workspace specially converted for that purpose. (DIS: "Context Is for Kings", "Brother")
Aboard Discovery, the engineering lab was highly classified and required a breath print for access. Immediately off of main engineering was a cultivation bay where Stamets was growing his own prototaxites stellaviatori spores. Aboard Discovery's sister ship, the Glenn, the engineering section was highly shielded and the hull was double reinforced, preventing transport after a spore drive disaster. (DIS: "Context Is for Kings")
Disassembly of spore drive equipment aboard the Discovery began in 2257, opening up the engineering lab with exposed conduits and machinery. Nevertheless, the spore drive was still operational. (DIS: "Brother", "New Eden")
Access and Jefferies tubes
Sickbay was located on deck four, and featured three biobeds. Similar to on the NX class, sickbay was much more brightly colored than the rest of the ship, being a near white color. (DIS: "The Butcher's Knife Cares Not for the Lamb's Cry", "The War Without, The War Within")
Transport and cargo
The shuttlebay contained a large platform, delineated by the vessel's insignia, which descended and rotated to enable access to a launch facility for landing pods. Four pods were stored there, leading to a single launch rail and exterior port. (DIS: "Brother")
The transporter room aboard Crossfield-class ships occupied a corridor room. The back of the room was a circular alcove containing the transporter pad. The steps of the transporter glowed red when in use. (DIS: "Choose Your Pain")
Crew quarters of the mid-23rd century tended towards spartan, with only minimal options for customization or decoration. Aboard Discovery, senior officers were assigned their own personal quarters, while junior officers shared quarters. (DIS: "Context Is for Kings")
Aboard Discovery, Lorca kept his own research lab, containing weapons and specimens that he'd collected (Harry Mudd referred to this lab as Lorca's "man cave"). Located on the lower decks of the engineering hull, this lab featured a holding cell and a window viewing starboard. (DIS: "Context Is for Kings")
Following Captain Pike's decision to move the captain's ready room to another location in 2257, the ready room attached to the bridge was converted into a science lab. Numerous pieces of scientific equipment (including a Vulcan data module) were moved into the section, the large window being separated into two ports by a computer terminal, and a large, transparent computer interface subdividing the room. (DIS: "Point of Light")
- Mirror universe
- ISS Discovery (NCC-1031)
The Crossfield-class ships bear some resemblance to the B-24-CLN, which was seen at the Surplus Depot Z15 in TNG: "Unification I". Both models are based off a concept USS Enterprise study model (the B-24-CLN actually being a reuse of the model) designed by Ken Adam and Ralph McQuarrie for Star Trek: Planet of the Titans.
Star Trek: Discovery Designing Starships explains the design process that went into developing the Discovery, including experimenting with different moving parts, hull surface colors and patterns, and ship proportions. Earlier models included short, thicker nacelles, such as a graphic that would be included onscreen in "Light and Shadows".
According to technical data prepared for the San Diego Comic Con in 2018, the ISS Discovery had seventeen decks, a crew complement of 180, a maximum warp of 8, two impulse engines (approximate warp factor 0.3), and a displacement-activated spore hub drive (approximate warp factor 1431). 
According to Star Trek: Discovery The Official Starships Collection, the Crossfield class is 750.5 meters long, consistent with the imperial equivalent of 2462 feet 4 inches (750.52 meters) given on a size chart in The Art of Star Trek: Discovery. This would be about 2.5 times the length of a TOS Constitution-class vessel and almost 100 meters longer than a 24th century Sovereign-class ship. However, The Official Starships Collection also claims that the size of the Constitution class was increased by a factor of 1.5 for Star Trek: Discovery, explaining why both ship types are of comparable sizes when they appear together on screen.
The Crossfield class is a playable ship in Star Trek Online, and has a small chance of appearing when a player purchases an add-on called the "Discovery Lock Box". The playable Crossfield comes equipped with the ability to use its spore drive to teleport the ship forward, unleashing a burst of mycelial energy that affects enemies' engines and leaving a payload of torpedoes to detonate in its wake, before teleporting back to its original position – evocative of the tactic employed by Discovery at Corvan II in "The Butcher's Knife Cares Not for the Lamb's Cry". The ability is referred to in-game as the "Lorca Maneuver". The mirror universe Crossfield is also a playable ship, available from limited-time "Infinity Promotions"; it has some subtle design differences to the prime ship and comes equipped with "Weaponized Helical Torsion" - the rotating discs of the saucer creating a buildup of mycelial energy which is then unleashed against enemy ships. The "Legendary Starship Bundle" released for the game's tenth anniversary in February 2020 features a 25th-century variant of the Crossfield class, christened the Glenn class after the USS Glenn, which comes with both abilities and can also be made to appear as either the prime or mirror Crossfield. The 32nd century refit was also made available as a playable ship from the "Discovery: Far From Home Lock Box" in May 2021, equipped with a cloaking device usable in combat and a Kwejian assault ship (similar to Booker's ship) for fire support.