The Dreadnought-class was an experimental class of dreadnought warship designed by Section 31 of Starfleet with the help of Khan Noonien Singh. The only known vessel of this class, the USS Vengeance, was launched from a secret facility orbiting Io in 2259. (Star Trek Into Darkness)
The Dreadnought-class was roughly twice the size of a Constitution-class starship. This class was designed to be operated by a minimal crew, one person if necessary. It had advanced weapon and propulsion capabilities allowing it to engage other vessels while traveling at warp velocities. (Star Trek Into Darkness)
The bridge of a Dreadnought ship was small and cramped compared to the more spacious bridge of the Constitution-class. Its design utilized highly advanced artificial intelligence (AI) systems to reduce the number of crew needed to operate the vessel. Under extreme circumstances, Dreadnought-class vessels could be operated by the captain single-handedly. Use of AI systems allowed for the operation of the starship's navigation and propulsion subsystems via voice commands. Also, in stark contrast to the Enterprise bridge, the Dreadnought's bridge was very dark – in lieu of bright lighting and shining white walls, the bridge was largely black, though still well lit. (Star Trek Into Darkness)
Engineering was designed so that it could run autonomously if needed. Like the bridge, the engineering section was cramped and painted in shining black. The interior featured a more refined design compared with the engineering section on the USS Enterprise – for example, there were no coolant pipes or mains directly accessible by the crew. (Star Trek Into Darkness)
The transporter system on the Vengeance could be operated from the bridge. The system could be used to site-to-site transport dozens of people or objects at the same time. It could for example transport all 72 photon torpedoes from the Enterprise. (Star Trek Into Darkness)
Transport and cargo
Khan was involved with designing the weapons for the Dreadnought-class. The weapons were significantly more advanced than contemporary Constitution-class weaponry. While most other Starfleet ships were multirole designs for combat, exploration and research, the Dreadnought-class ships were designed solely for combat. The deflector dish could be covered by protective armor plates while the ship was not traveling at warp speeds to defend the dish from damage during a battle. The ship was extremely durable and could remain intact even after the internal detonation of 72 photon torpedoes and a high speed collision with a city.
The weapon systems included an array of advanced phaser emitters. The powerful discharges from these weapons arced indirectly at the target and could be fired while the ship was at warp. Single hits could penetrate through the shields and cause major hull breaches to a Constitution-class starship.
The weapon systems also included massive swivel-mounted torpedo launchers that could be deployed from under the saucer section from behind protective armor plating. They could rotate and launch a volley of torpedoes at various firing arcs from aft to forward of the ship. A Dreadnought-class ship could also launch drones that in turn were capable of launching several photon torpedoes before crashing into a target. (Star Trek Into Darkness)
The Dreadnought-class featured two angular warp drive nacelles, unlike most Starfleet ships that had featured cylindrical nacelles. The Vengeance was described by Khan as having "three times the speed" of the Enterprise. The Dreadnought-class ship had the capability of tracking down and attacking a fleeing enemy ship while at warp speed. (Star Trek Into Darkness)
Screenwriter of Star Trek Into Darkness Roberto Orci suggested on Twitter that the USS Vengeance had a countermeasure against transwarp beaming. Hence, Harrison fled to Qo'noS instead of commandeering the Vengeance directly. 
Before Khan fired a barrage of the red arcing bursts of energy from the Vengeance, Sulu stated that the ship was locking phasers on the Enterprise. Before the two large cannons were deployed in Star Trek Into Darkness, Admiral Marcus ordered the targeting of all aft torpedoes at the bridge of the Enterprise. According to the novelization of the film, the two cannons were in fact massive banks of photon torpedoes, each holding an arsenal of more torpedoes than several ships the size of the Enterprise had combined.
According to the novelization of Star Trek Into Darkness, the advanced warp capabilities were called "Mark IV capabilities". They included special modifications to the warp drive and nacelles, that allowed a Dreadnought-class ship to momentarily exceed all accepted warp factors and catch up with a starship it was following inside its warp tunnel. According to a dossier of the Enterprise on the homepage of the previous film, the three times slower Constitution-class was capable of reaching speeds up to warp factor 8.  The terms "advanced warp capabilities" and "Mark IV" are similar to the prime universe classification "advanced fourth generation warp drive", that was according to the Star Trek Spaceflight Chronology (p. 180) attributed to the new warp drive and angular nacelles installed to the USS Enterprise in its refit for Star Trek: The Motion Picture, that according to the reference book also made the Enterprise more than three times faster compared to warp factor 8, in the warp scale, with a maximum velocity of warp factor 12.
Designing the Dreadnought-class
To devise the layout of the USS Vengeance for Star Trek Into Darkness, the movie's production unit conducted extensive studies of spacecraft designs, ultimately conceptualizing the vessel as an angular black-hulled leviathan depicted by Concept Artist James Clyne. "One of the first images that popped into my head," said Director J.J. Abrams, "was the idea of a big, terrifying stealth-like version of the Enterprise [...] It began as a visual concept of having a black ship." Abrams also conceived the Vengeance as a militaristic Starfleet craft, more than twice the size of the Enterprise. (Cinefex, No. 134, pp. 74-75 & 84)
The Vengeance went on to be built by a team at Industrial Light & Magic, which included Digital Model Supervisor Bruce Holcomb. They constructed the ship, one of multiple intricate CGI models in the film, to far outdo the capabilities of other Federation crafts. The Vengeance wound up being, noted ILM Senior Visual Effects Supervisor Roger Guyett, "about two-and-a-half times the size of the Enterprise." Guyett further remarked, "It was approximately 4,500 feet long, but we sometimes cheated that for dramatic needs." As could be expected, the Vengeance became in Guyett's words, "another enormous model with a huge amount of detail." (Cinefex, No. 134, pp. 84 & 75)
Combined with the darkness of space, the configuration of the Dreadnought-class vessel caused ILM difficulty with lighting the Vengeance. "The Vengeance design didn't lend itself to a lot of lights," explained ILM Lighting Technical Director Robert Weaver, "so we played with rim-light and specular values. We gave the ship 'Aztec' textures, similar to the Enterprise; so, anytime a light raked across the hull, it created interesting colors in the surface panels. We controlled those effects in specular mapping. We created different channels for different panel lights, the shaders wrote that information into EXR data files, and we could create as many channels as we needed. The Vengeance averaged three levels of specular, which compositors could adjust." (Cinefex, No. 134, p. 75)
A Dreadnought-class is briefly mentioned by William T. Riker in the novel Dark Mirror as a starship class that is the closest analog the prime universe Starfleet in the 24th century has to the heavily-armed and armored version of the Galaxy-class from the mirror universe.
The Dreadnought-class makes an appearance in Star Trek Online as a playable ship, released alongside the "Agents of Yesterday" expansion pack. However, as the term "dreadnought" in the game refers to a specific type of ship (as contrasted to "cruiser" or "science vessel"), the ship is referred to as a "Kelvin Timeline Intel Dreadnought Cruiser" (referring to its temporal origin, unique traits, and performance characteristics), and more specifically the Vengeance-class. The ship possesses rapid-fire broadside phaser batteries and can launch automated assault drones to act as fighters. Unlike the on-screen version, the in-game version of the ship is also equipped with a cloaking device. A later update also allowed for a visible name and registry number to be displayed on the hull.