Theurgy

Introduction

Theurgy is one of the three main types of magic used in the Grand Empire of Karadia. While the much more common thaumaturgy uses naturally existing mana that's processed by the practitioner into a spell, theurgy is something that is almost entirely independent from their users. The theurgists instead borrow powers of the higher beings, and their 'spells' are pretty much immediately (and precisely) answered prayers.
This is both the theurgists' strength and weaknesses. Their prayers are many times stronger than spells and capable of achieving things that no spell is simply capable off - some of the stronger ones are best described as a localized reality warp, capable of causing practically every imagineable effect while totally ignoring the established rules of thaumaturgy. But there is no rose without a thorn, and while a powerful theurgist can be a complete game-changer on the battlefield, it greatly depends on many factors. And then, there is the other price for the answer to your prayers...
Theurgies are useful because they can do things that thaumaturgy cannot - mostly by being way more powerful than it can ever be. No mortal being can be exposed repeatedly to such powers without being altered. Every casting of a prayer or benediction and every invocation of a miracle make you less and less of a mortal. Of course, whether that's good or not in the eyes of general population tends to depend on your patron - and this isn't a secret, so those who use theurgy tend to consent to such outcome.

Three Types of Theurgy

The High Gods

The imperial divines are generally the safest option when it comes to choosing who to dedicate yourself to. They do not want their theurgists to burn their mortality out too quickly, and had them master the art of using external conduits for their theurgies. This means that their prayers are relatively safe for the user, even the stronger ones. However, there is still some influence to be considered, which will - if one lives a live of true devotion and uses their prayers and benedictions repeatedly - lead to an ascension event.
Every high god has a separate list of prayers and their own dedicated priesthoods who can learn them. Not all of them are combat-oriented, for example the prayers to Hortulanus are a backbone of the imperial agriculture, capable of restoring fertility of depleted soil and improve the plot's yield by a few dozen percents if applied regularly.
The combat prayers are most common among the priesthoods of Honor, Bellaminae, Sol, and Audacia, with priests and priestesses of Caritas also being notable for its defensive and healing abilities. However all priests - regardless of their allegiance - will be capable of at least a few self-defense benedictions. Those are usually light-themed in nature, being gifts from Sol, and to a lesser degree Mors, with flame being the second most common theme thanks to Honour. Physical amplifications (that allow them to actually fight some martial artists, at least depending on the priest) are third in the line, usually attributed to Bellaminae and Audacia.
The theoretical greatest strength of the theurgies is that they do not require mana. Benedictions can be cast freely, with the only problem being a very modest increase in attention. However, to cast prayers, you require favor of your patron, which is recharged by performing appropriate rituals and doing appropriate works (including moral decisions and just literally working). However, benedictions are usually somewhat weaker than comparable thaumaturgies.
And it's not compatible with thaumaturgy. They are exceptions here, but usually on the side of the hierarchs.
Divine favour is always in short supply. Rather than being perpetual dispensers of divine thunders of evil annihilation, most theurgist will carefully (sometimes too carefully) choose when to use their powers. The powers that they have freely available to them - namely the way weaker benedictions - are simply underpowered when compared to what thaumaturgists are capable off (and you still need Favour to unlock them). On the other hand there are also some theurgists that spend their entire live locked down in the sanctuaries, amassing Favour - which means that when they leave the sanctuary, they are more akin to living weapons of mass destruction.
Only the exarchs have benedictions and such a detailed system of prayers. Hierarchs partially mix thaumaturgy with theurgy, their magic operating under the rules of the former but having an element of theurgy to them. However, some of them (especially the ones of Nine Hordes, Rapturous Ecstasy and Shadowlight Covenant) have a few theurgies that work more akin to prayers.
Those theurgies are usually gifts from the High Gods themselves to their notable followers, granted (permanently) after achieving something great.
Anarchs do not care about mortals enough to join the theurgical framework.

The Subtypes

Ascendants are the end-result of someone overdoing the theurgies of one particular exarch to the point where their body simply cannot resist the fleshchanging effects of powerful divine energies that they were exposed to. Of course, with the exarchs being what they are, the change is ultimately benevolent: Ascendants are silverskinned humanoids who are closer to daemons than mortals, are capable of unleashing incredible devastation upon their enemies (or to do stuff like make the soil stay fertile and have things grow on it so fast that you can harvest few times a year).
Chosen Ones are the most powerful of already extremely powerful theurgists. They never 'learned' their powers - instead they were personally exalted by the one of the High Gods. That they got to meet in-person (at least technically, it happens while dreaming). The result is the absolutely overwhelmingly powerful mortals, in case of the Chosen Ones of the combat-oriented gods also doubling as simply the most powerful mortals at all.
High Ascendants are the end-result of a Chosen One. Who, through either casting their special miracles for a long of time or by dying (after living) in a way that pleased their patron enough. In the end it's hard to see a Chosen One not end up as a High Ascendant. The result is goldskinned humanoid who are an equivalent of strongest amongst demigods in firepower.

Tools

The imperial theurgists are safest among their tradesman precisely because they aren't the channeling the power of their patron through their body, and instead use external catalysts. Those are typically various holy symbols - occasionally swords or staffs) who were properly treated and sanctified by a presence of a demigod or a high ascendant in one of the sanctuaries of the Imperial Cult. Those items act as conduits for the divine power, and greatly lower the speed at which mortal theurgists stop being mortals.
The imperials have also developed a wider array of items typically used through theurgies, including robes woven from a blessed cloth (that can actually resist an impossible ammount of punishment, surpassing even average plate armors) and more classic armors and weapon from metals that were properly treated to better conduct theurgies.

The Monotheist Gods

All known monotheist gods from the neighbouring cosmologies possess certain form of religion-oriented magic. They are mechanically closest to the theurgy, and has been often classified as part of it. Their theurgies tend to include direct channeling of divine powers, but the change that's eventually brought is typically mostly benevolent.
One thing has to be said - they are POWERFUl. Some of those cosmologies don't even have thaumaturgy, if only because they don't see a reason to have it. On a neutral ground, monotheist theurgy will always triumph over the polytheistic one, if only because in their cosmology, monotheistic god is an equivalent of ALL polytheistic gods at once, making them operate on a completely different level.
However, those gods are also usually more personally connected with their worshippers. As a result, prayers are seen as just something you do on the inside, to communicate (one-sidedly) with your god. As a result, they don't have such magical results as what exarchs (who don't have non-magical prayers, and instead have a variety of rituals and offerings) have.
As a result, their theurgies are usually referred to as miracles.

Subtypes

Too many to describe in details - these are three completely different religious systems, and three different cosmologies to consider. It will be best done in a separate article concerning these vastly different cultures.

Tools

Situation varies. Too many to describe all regional variants on that field for three different cosmological systems.