Powers and Technology: Magic is a science based on 'chords', which are akin to internalized music-like incantations. The 12-step chord is the basic foundation for magic; variations on this are known to be used by beings with highly exceptional skill, usually beings from the Backyard (Izuna, Valentine) and can be taught. These chords can be thought of as 'data entry' which accesses the power of another dimension called The Backyard, a world that you could say is like the computer code to the human world and equivalent of Makai or Netherworld for other worlds; youkai and other beings, usually referred to as Exceptions or Others are born and usually reside in various parts of The Backyard (example: Underworld Hill, the home of Izuna and his youkai friends; Makai, home of Slayer and his 'Other' comrades). The ability to enter and access this data is dependent on one's stamina, so the ability to wield magic varies from person to person. Gears, as artificial youkai, have a preternatural disposition to access magic. Some humans (examples: Ky Kiske, I-No) are also born with naturally high skill with wielding and controlling magic.
Magic in the Guilty Gear world is based upon the 8 Phases/Trigrams/Elements in I-Ching divination: Fire, Wood, Earth, Mountain, Water, Wind, Heaven, Valley (disputable; it's stated to be based on the basic 5 phase version in another canon source. In this same source, Ki is stated to be one of the elements... so it's sort of questionable that it's only 5.) Ki is noted to be used primarily only be those of Eastern descent; the use of Ki by Westerners is incredibly rare and only 2 Westerners are known to use it: Kliff Undersn (First Commander of the Holy Order), and Chipp Zanuff (trained in shinobi arts). Ki may be able to be attributed to the Heaven or Earth trigram.
Elemental choice in magic use is usually determined by preternatural affinity; some elements are also more easy to control. Fire is stated to be a common and easy to control affinity; Ki is a common affinity in those of Eastern descent; Lightning is a very rare and difficult to control affinity. Examples of affinities in characters: Ky Kiske, Sin Kiske: Lightning; Sol Badguy, Axl Low: Fire; Baiken, Anji Mito, Chipp Zanuff, Jam Kuradoberi: Ki; Dizzy: Water(? possibly also Wind).
Most magic in the GG world is based on the 12 step chord and produces basic magic wielding; the use of dimensional gates, time travel, Master Ghost, and tribe summons is considered outside the normal range (the Soul Sinker system- the use of Master Ghosts and tribes- was taught to Sol and Sin by Izuna; used naturally by Valentine.) Soul Sinker combat can be considered equivalent to the use of Personas; literally a manifestation of one's soul. Master Ghosts and tribes are usually unique to the user.
Any technology that uses fossil fuels, nuclear power, or most any other source we are familiar with in real life are considered Blacktech and are strictly outlawed save some use in the floating, isolationist nation of the Zepp Republic. Oversight of blacktech restriction is the job of the International Police Force and ultimately the United Nations; however certain groups such as Zepp, the Jellyfish Pirates, the Post-War Administration Bureau, and the Assassin's Guild, as well as some corrupt sectors of the Police Force itself, still seek and use Old-World blacktech weaponry, especially firearms. The power of blacktech is feared as being once greater than any magical tech or even Gears (specifically nukes); however Gears are shown to have some resistance to blacktech weapons (examples: Sol Badguy, GGX Drama CD; Commander Dizzy, Side Red/Black AU.)
The IPF is known to be in possession of a magically-powered attack satellite akin to a magical nuke, codenamed Last Resort. It has the power to destroy a Megadeth Gear in one shot, but the radiation caused by its blast lasts 100 years. (Source: Lightning the Argent novel; think of it as conceptually similar to Blazblue's "Take-Mikazuchi" Nox.)
Outrage: An anti-Gear weapon created by Frederick. Comprised of 8 Jinki, or Sacred Treasures, which each operate on their own as seperate weapons. They were entrusted to the United Nations and from there, have made their way to various holders. Known pieces: Fuuenken/Fireseal (Owner: Sol Badguy); Fuuraiken/Thunderseal (Owner: Ky Kiske); Zessen/Stopping Fans (Owner: Anji Mito); Senga/Flashing Fang (UNCONFIRMED Owner: Slayer); Kojouhaku/White on the Lake; Ekitoku/Increasing Fervor; 2 other unnamed pieces.
Additional info here. (But keep in mind the 8 Phases are laid out incorrectly here.)
Species: Human, Gear, Gear derivatives (Kinjuu), Ghosts, Vizuel?**, Vampire, Youkai, Other/Exceptions (these are very case by case though and Vampires and Youkai are considered 'Others' as well. Beings born in the Backayard (Valentine) and beings that have gone 'beyond human'- canon examples Faust, Sharon, Raven- count in this category.)
**Very little is known about the Vizuel apart from that they are a sentient class of beings that chose to side with Valentine. Their origin may be the Backyard but it is not certain. They are best considered Exceptions.
Special note about Race: In Guilty Gear, Japanese people are considered rare specimens to the point that most normal people alive in the present of GG do not even know what 'Japan' or 'Japanese' is. They are also somewhat both feared and desired for their supposed powers, especially potential and prowess with Ki. As such, suspicion of being Japanese will be met with possible fear, confusion, or hostility. More notes about the situation of people of Japanese descent are below.
Specific information on classes of Gears here. The Backyard: A dimension adjacent to the human one. It is described as 'the programming code of which the resulting program is our own world'. Magic is actually the form taken by energy accessed from this world by rewriting the data of the Backyard. Scientists first theorized its existence in 2010. Most beings are unable to enter the Backyard due to the immense pressure of this world; beings born here, as well as some particularly powerful magic-based and wielding beings are able to enter without being destroyed.
Beings known to have been born in the backyard: Valentine, Izuna. Slayer resides here, but was not born here. Faust, with his dimensional magic, has been thought to be able to access here; same possibly with I-No. That Man also is able to access this place. Sol is able to travel through this place.
The Cube: A man-made object (created by That Man) residing in the Backyard which contains the data for the existence of Gears; in particular it contains the 'source code' of Sol's prototype Gear DNA. Justice's Commander Gear cells are needed to access it. Sol and That Man are the only ones able to affect it without Justice's DNA.
Government/Politics and Organizations:
The Sacred Order of Holy Knights (Seikishidan): The military force put together just after the turn of the 22nd century to combat the Gear armies; its primary supporters are the Roman Catholic Church and the United Nations and both men and women take part. A tournament was held at that time to put together the beginnings of the army and determine the strongest fighter who would lead the Order- the winner of this tournament was Kliff Undersn, and he became the first Commander of the Holy Order. In 2172, Kliff seeks out Sol Badguy to recruit him into the Order. In 2175, Ky Kiske takes over from Kliff Undersn as Commander of the Order at age 16. Sol Badguy deserted from the Order, stealing the Fuuenken at that time. The Order was disbanded in 2176 after the sealing of Justice, however retired knights still pop up from time to time- some, like Ky, joined the police force to continue serving the peace; others became priests or bounty hunters.
More information here. Known (/former) members of the Holy Order: Ky Kiske, Sol Badguy, Kliff Undersn, Tess Undersn (Testament pre-conversion), the priest who looks after Kliff's grave near the Demon's Grove, the priest who cares for Marina and Solaria in Lightning the Argent; various police officers in Ky's unit.
International Police Force: A police force historically controlled by the United Nations. After the war, many former members of the Seikishidan joined the police force. They take part in operations pertaining to the sealing and disposal of remaining Gears, recovery of blacktech, and illegal operations by large organizations such as the Jellyfish Pirates, Assassin's Guild, and political relations with the Republic of Zepp.
Known members: Ky Kiske (Captain)
The United Nations: Pretty much the central political force in the world of Guilty Gear, it controls most of Europe, at least. The IPF is under their control.
Post-War Administration Bureau: A group that was perhaps founded by the UN during the Crusades, perhaps for the purpose of anti-Gear weapon development, which was supposed to have been disbanded at the end of the war due to corruption, but continued to operate in secret. A shady group which makes moves to collect various data from key players in the Guilty Gear world for unknown purposes, but appear to have interest in developing new weapons and gaining political power.
Known members/agents of the PWAB: "Crow"/Kuruwaba Kurou, Robo-Ky units, Justice clone units.
The 3 Kingdoms: Not much is know about the 3 European kingdoms, but one of them is the United Kingdom of Illyuria. In 2183, Ky Kiske is "elected" King of this nation-state against his wishes by the manipulations of an unknown player. He remains at this post through 2185, in which Overture takes place. It comprises of a large part of Europe. It is shown in 2185 that the United Nations is not on friendly terms with Illyuria's monarch, and has been making threats to depose him if he does not meet their demands (which, he says, essentially comprise rendering him a puppet leader).
Republic of Zepp: A seclusive and somewhat xenophobic floating continent-nation that exists high above the clouds, away from the eyes of the rest of the world, founded by those who believed that Blacktech still had its uses and should not be totally discarded. Therefore, Zepp is the only place where Blacktech is freely and widely utilized. Until about 2180 it was under the control of slave-holding dictators, however a revolt following the Second Holy Knight Tournament overthrew this government and installed the general Gabriel as its leader. Zepp generally does not interfere with the matters of the below world unless they see something they want, in which case they tend to use their powerful blacktech weaponry and battleships to strongarm the other governments.
Known citizens of Zepp: President Gabriel, Potemkin.
A-Country: The remnants of the United States of America. For a long while, had ties to the Assassin's Guild, however the nation's new young genius President, 17 year old Erica Bartholomew, finally broke off these ties with the help of Chipp Zanuff.
Known citizens of A-Country: Chipp Zanuff, Johnny Sfondi (born there), Sol Badguy(? born in the USA originally)
Assassin's Guild: An ages-old shadow organization originally founded by Slayer to keep the balance of power in the world and act as 'divine punishment'. However, by the time of the end of the Crusades, it has grown corrupt. Around the mod to late 2170's, the leader of the Guild was a man called Zato-1; at this time, then-assassin Millia Rage made an attempt on Zato's life before deserting the Guild. After Millia kills Zato in 2180, Zato's right hand man and admirer Venom takes over control of the Guild. The guild is responsible for several shady operations in the series, including sabotaging the operation which made Baldhead/Faust go insane, and the murder of Chipp Zanuff's master Tsuyoshi.
Known members of the Assassin's Guild: Slayer (founder), Zato-1 (former leader, deceased), Millia Rage (former), Venom (current leader), Tsuyoshi (as a double agent for the IPF), Volf (Tsuyoshi's murderer; killed by Venom for failing to kill Chipp Zanuff in Butterfly and her Gale).
Japanese Colony: The 'colony' (really more of an internment camp) where the remaining bearers of Japanese ancestry are kept hidden from the rest of the world by a powerful kekkai barrier (provided, partially, by Anji Mito's Zessen fans). It was set up and overseen by the UN and IPF.
Known residents: Baiken, Anji Mito, Chipp Zanuff (occasionally).
Jellyfish Air Pirates: A criminal organization comprised mostly of orphaned young girls and women with the exception of their captain, Johnny Sfondi, who recruits them. Their activities generally involve heists of rare artifacts, money, food, and supplies which are then used for the upkeep of their fleet with the remainder being distributed to poor and needy villages around the world. The organization is made up of several sub-fleets of airships apart from the flagship, Mayship, which holds the most powerful members of the crew, including Johnny himself.
Known members of the Jellyfish pirates: The Mayship crew: Johnny Sfondi, Janice (a cat), Febe, March, April, May, June, July, August, Sephie, Octy, Novel, Dizzy, Mrs. Leap. Bridget, a young boy, is an honorary member.
Landscape and Travel:
Airships: Enormous boat-plane like ships that use magical engines and wind spells to fly. Most long-distance transportation makes use of these ships. The Holy Order, IPF, Republic of Zepp, and Jellyfish Air Pirates are a few organizations who run their own fleets of these ships.
Apart from airships, travel is made on foot in the Guilty Gear world. Trains, cars, and airplanes have never been mentioned nor seen. Cars are specifically mentioned to no longer exist, and parts of them are rare blacktech contraband.
Society/Civilization:
Apart from a few known remaining major cities: Paris (which was the most well protected as the headquarters of the Sacred Order of Holy Knights), small parts of London and Moscow- most of the world was completely razed by the Gear armies during the Crusades. The nation of Japan was literally wiped off the map; Eastern Asia and most of North America sustained the heaviest damage, while Europe was the main focus of the activities of the Seikishidan and thus the most protected, although even that did not spare it much. Therefore, society post-Crusades has devolved to a point something like a mix of pre-WWI European farming villages and the Dark Ages, with only minimal amounts of (magical) technology to prove civilization ever advanced.
Beliefs and customs in the post-Crusades world- especially in Europe- bear heavily religious (mostly Christian/Catholic) overtones, owing to the prevalence of the Holy Knights as humanity's last hope for the past 100 years and likely due to various superstitions developed in the wake of the 'demons', the Gears. Suspicious abilities and inhuman appearance or ability is usually met with fear and hatred, often suspicion of being a Gear or otherwise bad omen.
Medical technology has also devolved. Disabilities such as blindness, sicknesses caused by lack of basic hygiene have risen in the wake of limited medical knowledge and supplies post-war. This is why Faust, the demon doctor, is so highly regarded for his near-prophetic knowledge of medicine (despite his ...quirks). Unfortunately, this is also taken advantage of at times, such as when a corporation called Blackard used unwitting citizens of a village near London to test new Gear-conversion methods by fooling them into thinking they were receiving medicine. (Lightning the Argent)