Wizards
The Academy
Once upon a time, there was a single, dominant wizard order: the Order of Hermes. They began as a cult of greek philosophers seeking universal truths through sacred geometry. Their path to dominance was helped greatly by the appropriation of Greek culture by Rome, who spread their art throughout the known world, whereupon it mixed with the many and diverse magical traditions of European, Asian, and African natives.
The rapid collapse of the Western Roman Empire led to a fracture in the magical traditions of Europe and North Africa; from their common base as inheritors of the Hermetic tradition, they diverged, and wouldn't be reunified for a thousand years. Meanwhile, the Eastern tradition continued to build on the original Greek, but with an increasing influence from both Near and Far East. This tradition never quite reunified with the rest: today, it has evolved into the Magi of the Moon and Star, and is based in Istanbul.
In the 17th century, after centuries of inquisition and witch hunts, it seemed necessary for the practitioners of Europe and North Africa to reinvent themselves, both for mutual protection against organized and disorganized religious persecution, and to distance themselves from the associations which led to that persecution in the first place.
Crucial to this effort was the Genoan wizard Federico Barcello, who was inspired to rid the wizardly profession of all trace of Necromancy and demonic worship. He sought to divest wizardry of its "barbaric past", of association with paganism. While he himself was a devout Christian, other reformers, without whom the movement would not have been possible, preferred a more mystically-neutral approach, ridding all direct association with any religion.
From this effort arose the Academia Arcana Universalis, a unified network of wizardly traditions, schools, and orders. Not a school in and of itself, the Academy provides high-level guideline on what should and should not be taught, and how so. Likewise, it establishes a common defense--from practices on security and necessary concealment from public scrutiny to shared assets, magical and otherwise, for mutual protection. Atop the Academy sits a High Council, made up of the eldest and most distinguished wizards of all the lands, who decide all matters of policy and justice.
The wizards of the Academy have taken it upon themselves to protect the world from all manner of magical threats, lest they find themselves at the business end of another inquisition or series of witch hunts. To that end, they employ an order enforcers, the Order of the Eldritch Flame, or, commonly, the Eldritch Knights. These specialized wizards combine the art of sword and sorcery into a finely-honed craft of war. Not only do they enforce the Academy's strict Laws of Magic, but they also serve as the vanguard when the Academy itself is threatened by rival organizations.
Once intended to unite only the disparate successors of the Order of Hermes throughout Europe and North Africa, the Academy has grown to encompass the vast majority of all organized wizardly orders, including the august, ancient orders native to China and the Far East, which found themselves unprepared for the rapid changes of the 20th century.
Today, anyone who bears the title of "Wizard" is, or ought to be, a member of the Academy. He may well also be a member of an older order, such as the Magi of the Moon and Star, but such titles are often only ceremonial, as the old laws and power structures of those orders are all but dissolved to ensure compatibility with the higher order of the Academy.
Not all of the elder orders have been so assimilated...some small, proud few insist on their independence, relying on secrecy to keep the all-encompassing Academy at bay.
Other Orders
The Order of Merlin
The Order of Merlin is ostensibly the very same wizard order to which its titular head belonged. He himself is thought to have been a follower of a much older tradition, now lost to time, and the ravages of the Inquisition. Now, it bears his name, and his purpose.
Practitioners of the order believe they are meant to guard the realm of Albion (an earlier name for England) and its True King, until such time as the throne is restored. Not only, they claim, is the True King the rightful lord of England, but he was also meant to usher in a new era of enlightenment. His failure, due to treachery from within and without, indirectly allowed the Dark Ages to occur. Though they have now ended, the Order maintains a greater calamity awaits, and mankind is doomed without the True King's guidance. No longer does his mandate extend merely to England, but to the whole world.
Once, the crown of England employed wizards, diviners, and sages of all kind. Though they became scarce as Christianity took root, they never quite vanished--that is, not until the death of Elizabeth I of England, when the Catholic James I expunged all trace of England's pagan past. Until that time, members of the Order guided the British monarchs; since then, they have taken refuge in the New World, and expect the True King to emerge there.
The Hermetic Order of the Golden Dawn
In the 19th century, there was a great surge of public interest in the occult. With no input or guidance from the Academy, many private citizens turned to whatever sources they could find, in pursuit of magical knowledge. Some, such as the members of the Hermetic Order of the Golden Dawn, found it.
Generally speaking, wielding "pure" magic as wizards do (that is, pure of any influence from outside entities), is a very difficult pursuit requiring many years of intense practice and meditation merely to grasp the fundamental concepts. Few are willing to wait so long, and in the 19th century--much as it was in centuries past--there are plenty of outsiders willing to empower those who seek their aid...for a price.
As the High Council would have it, practitioners of the Hermetic Order are warlocks, violators of the Laws of Magic, and enemies of wizardry and mankind. Unfortunately, they also tend to be populated by some of the most powerful and visible members of mundane society, and as such, are difficult targets for the Eldritch Knights, particularly in an era where technology allows mortals to rival the power of wizards.
Today, the Hermetic Order, and many other, smaller orders, practice arcane traditions, some of which are genuine invocations of outside power, while many others are nonsense planted on the racks of bookstore shelves by wizards; precious few in these orders have access to true power, but those who do enjoy free reign in human society, easily rising through its ranks with the help of their patrons...until the price is ultimately exacted upon them.