If your interested in the European Cavalry from 1870 to 1914, I've got a blurb from a previous answer with some details, as well as sources to follow up:

A. J. Ecchevaria and especially Stephen Badsey, have written about the revival of the European mounted arm at this time after the firepower revolution appeared to have placed them in doubt (Badsey's [thesis] (https://www.repository.cam.ac.uk/bitstream/handle/1810/244878/Badsey12201.pdf?sequence=1&isAllowed=y) is excellent for covering the controversy). Cavalry was now to be highly trained, kept in large corps and divisions when the armies clashed but dispersed to scout and reconnoitre when on the march, and ideally should be capable of dismounted "fire" and mounted "shock" action, the epitome of this being the British Cavalry in WWI.

This question could do with some narrowing down as "developments in European cavalry warfare 1500-1945" would be a pretty damn hefty tome to read and a beast of a reddit post to write. I'll gladly help out but "From knights to cavalry patrols in WW2" is going to be my life's work, not a tuesday reddit post. :)

A reply to /u/HarryCochrane

The caracole style cavalry, discharging their guns while rotating, was a reaction to the concentration of pike infantry. They force less disciplined infantry to discharge their weapons at longer range, such that they could close in and fire into infantry formation at closer range, protected by their armor. They were believed to be largely a harassing force, seeking openings in enemy formations and rarely charging in. Although when they did have a chance to charge into disrupted formations, the effect was terrifying.

There are still arguments as to what Gustav Adolph's cavalry reform was truly like in practice. The popularly cited claim, based on Michael Roberts' Military Revolution lecture, is that he rejected the Caracole pistol-wielding cavalry who would harass infantry units, and instead insisted on cavalry charging head on. At the same time, he ordered cavalry squadrons to be supported by firearms platoons to increase their power. These two points seem to be contradictory, as pointed out by many authors. In order for the musket platoons to be in effective range, there would not be sufficient range for the light cavalry and horse that the Swedes and Finns used, to charge effectively.

Sweden's own cavalry reform was due to their experience in fighting Poland-Lithuania. To quote a post by /u/ParkSungJun here.

The Swedish cavalry simply didn't have the power to engage the Polish lancers and shattered, exposing the infantry's flanks and causing a total collapse of the line. This battle among others inspired the Swedes to change their cavalry tactics from the sword and pistol reiters to lance equipped chargers. However, the main disadvantage of the hussars was that due to the need to maintain powerful war horses, only some of the Polish nobility, or szlachta, were able to maintain them, thus limiting their numbers and use. In addition, as infantry rate of fire started to increase, cavalry as a whole became less effective, especially the frontal charges favored by the Poles.

As a note, Swedish and Finn cavalry used lighter horse and lighter armor than German reiters or cuirassiers, so it was not surprising that Swedish copying of German tactics didn't work as well.

Recent scholars have argued that towards the end of the Thirty Years' War, decisive cavalry engagements tended to be close-quarters battles starting with the discharge of guns at close range and then continued with sabers. This focused on flanking enemy formation and then attacking them from the flank or rear at the same time that pressure was applied by friendly infantry units from the front.

Essentially, the cavalry became focused as a shock assault unit using mobility to attack the flanks or rear, a trend that continued into the Napoleonic era. It is telling that at the Battle of Lutzen (1632), Pappenheim's Imperial cavalry did not rely on the caracole, but rather on dedicated assaults upon Swedish cavalry. Given their heavier horses and armor, the Imperial cavalry was able to push Swedish units back. These charges cost Pappenheim his life, as he was hit by a cannon ball in the chest. But the dire situation forced Gustav Adolph to ride to his left to stabilize the situation, where he was shot by an Imperial pistolier in the back from very close range. Caught in his stirrup, another pistol shot hit him in the head and he lost his life in the battlefield.

So, for all the theoretical reforms that Gustav Adolph advocated, and deterministic comparative statements, we have to carefully examine contemporary reports of battle and longer-term trends.

• Jorgenson, et al., "Fighting Techniques of the Early Modern World," ISBN: 0-312-34819-3, 2005.

• D. Parrott, Strategy and Tactics in the Thirty Years' War, in "The Military Revolution Debate".

• D. Eltis, The Military Revolution in sixteenth-Century Europe, ISBN 0-76070-765-0, 1995.

The main development was really the response to the growing prominence of pike formations and firearms. Pike formations that held their ground were generally impervious to cavalry assault and firearms could inflict casualties before the cavalry could even make contact.

With regards to armies around the 1500 period (including Gustavus Adolphus), one of the main developments was the introduction of pistols and muskets to cavalry formations - with the later in particular serving as mounted musketeers (called dragoons). This gave the cavalry some ability to fight pike formations from a safe range.