The Empire from Warhammer Fantasy is heavily based on the Holy Roman Empire. This is obvious as soon as one looks at the map. All cities and provinces have German-sounding names (Averland, Osterland, Ostmark). The capital of the Empire is the city of Altdorf, which translates into “Old Village”. It is bordered by the nation of Kislev to the North and Bretonnia to the West, both of which are based on the real-world nation – specifically, Russia (Kislev is named after Principality of Kiev), and France (Bretonnia is named after French province Bretagne).
Politically, the Empire is a confederation of ten large provinces: Averland, Hochland, Middenland, Nordland, Ostland, Ostermark, Reikland, Stirland, Talabecland, Wissenland, each of which is ruled by an Elector Count.
The Empire is nominally ruled by the Emperor which is chosen by majority voting of various electors. The electors are the ten Elector Counts, the Grand Theogonist of the Sigmarite Church, the two “Arch Lectors” who are also clerics of the Sigmar church, the High Priest of Ulric and the Elder of the Moot (representing the halflings). Karl Franz, of the Holswig-Schliestein family, is the current Emperor. The Emperor is usually also one of the Elector Counts; Karl-Franz is the Elector Count of Reikland.
This, again, is similar to the Holy Roman Empire, albeit with one specific anachronism. The ten large provinces appear to be based on the stem duchies of the Eastern Francia. It was the dukes of these stem duchies that, after the death of the last Carolingian, had elected the next Emperor. Stem duchies were duchies based on tribal identities. These stem duchies were abolished in 1180. and replaced by the territorial principalities based on the feudal principle. The title of the prince-elector however was only established in 13th century. Fact that there are State Regiments suggests that the provinces are indeed territorial instead of feudal, and while nobility may have a lot of power, government is still centralized (so Late Feudalism instead of High Feudalism).
Another similarity to Holy Roman Empire lies in the fact that some of the more important cities have managed to achieve status of city-states due to their importance (Altdorf, Nuln, Talabheim, Middenheim). These are the equivalent of the Holy Roman Empire’s Free and Imperial Cities, a term which was used to denote a self-ruling city that had a certain amount of autonomy and was represented in the Imperial Diet. Free cities held the Imperial Immediacy, meaning that they were subject only to the Emperor and not to the territorial prince, and thus could indeed be classified as city-states.
Armies of the Empire are primarily infantry-based, and comprised of various troop types. These include spearmen, swordsmen, halberdiers, crossbowmen, archers, but also the cannons, handgunners and pistoliers. This conglomeration is actually drawn from real armies of the Holy Roman Empire, albeit over a period ranging from 15th to 17th centuries. Much like armies of the 17th century Holy Roman Empire, majority of the Imperial armies are comprised of infantry, with some light and heavy cavalry. Major advantage over the Holy Roman Empire is presence of mages and tanks.
Combination of pikemen, swordmen / halberdiers and arquebusiers / crossbowmen is reminiscent of the early tercio or pike-and-shot formations. Pikemen provided protection against the cavalry charge and enemy pikemen while arquebusiers thinned out enemy ranks with volleys of lead. Swordsmen, called rodeleros, would help break the deadlock when pikemen came face-to-face, but they were phased out as guns got better. In Switzerland and Germany, halberdiers were used in place of the swordsmen. Tercio was also supported by the heavy cavalry, which dropped the lance in favour of several pistols.
Empire has excellent, though not very numerous, cavalry in the form of its Orders of Knights, which are led by Grand Masters. This might be a reference to the Teutonic Order, which conquered lands of what later became Prussia from Poland. Knights are lot more powerful and important than in historical 17th century Holy Roman Empire, largely because none of the enemies the Empire fights have the discipline necessary to hold the pike wall.
In terms of artillery, Imperial artillery is again based on the 15th to 17th centuries. Empire’s cannons are muzzle loaders that are rather large by historical standards. This could be for two reasons: either because of the magical fortifications, magical beasts, or both. Smaller artillery is used against infantry, and is based on the volley guns. Lastly, Empire uses Helstrom rocket battery which is based on the early 19th century Congreve rockets, which used stick to stabilize themselves in flight, or maybe Korean Hwacha, a multiple rocket launcher on wheels from 15th century. I have no knowledge of Holy Roman Empire using rockets, but cannon technology is comparable to the Empire of Man. Where EoM differs is their usage of oversized cannons, possibly due to the enemies also fielding oversized fortresses.
Lastly, Empire uses steam tanks that are more magic than steam. Steam itself is not efficient enough to propel a relatively small ground vehicle such as a steam tank for a long time, unless it is on rails (and steam locomotives were hardly small). Worse, the tank shoots its cannons with compressed steam, which would have a doubly negative effect of a) making shots rather weak compared to gunpowder counterparts and b) heavily cutting into tank’s ability to stay in the field as valuable steam is expended to throw stuff at the enemy. Still, the Empire is heavily forrested with many bodies of water, so fuel for tanks is literally everywhere. The greatest problem with the tanks are their wheels. Imperial tanks are big, armoured boxes… on wheels which appear to have been stolen from an oversized horse carriage and would cause the thing to sink into anything that is not a paved road or hard soil. Steam cannon is likely used because proper cannon would shatter the wheels and/or axles. And in the Age of Sigmar, they can actually produce the damn things.
Flagellants are one of the paramilitary units in the Empire. They are civilians who beat themselves almost dead in penitence for their sins and sins of the world. Historically, they were heretics mad at the Church who wanted to cleanse themselves from sin, and thus were burned at a stake. The Empire tolerates them as cannon fodder instead of burning them at the stake, but other than that they are just as inept as the historical flagellants. And these could not fight all that well, or at all.
Free Companies fill the role of “irregular” units. These are collections of militias, mercenaries, peasants pressed into service and local citizens. Except for the name, however, they have little in common with their historical namesakes. Historically, free companies were companies of mercenaries recruited by private employers (and thus “free” of governmental oversight). Free Companies as described have more in common with various Crusader armies raised by the Kingdom of Hungary during Ottoman Wars, which included mercenaries, freelance knights, foreign contigents, armed peasants and more.