Humanoid warfare began with light infantry - quite undisciplined groups armed with melee weapons.
"Soon" thereafter (likely hundred thousands of years later, but we know almost nothing about that period) missile infantry joined the fight; slingers, javeliners, bowmen and possibly blowpipe warriors.
It seems that a form of cavalry appeared next; chariots. The earliest use of chariots was in the missile cavalry role, as an elusive platform for missileers. Later on riding was used in combat and light cavalry began to take over that role at lower cost, better robustness and cross-country characteristics.
At about that time heavy infantry - protected by armour and disciplined in the use of battle formations - was introduced and began to dominate warfare in Greece.
The late use of chariots was apparently focused on the heavy cavalry role; shock attacks, even armed with scythes on the axles. They did finally disappear - simple rider cavalry proved superior also in the heavy (shock) cavalry role.
At this point it's interesting to have a look at ancient Hellenic warfare.
It was early on quite formalized and restricted by rules until the civilization-fracturing Peloponnesian War (the ancient equivalent to the First World War - Greece was incapable of further civilization advances afterwards!). Heavy infantry in phalanx formation moved against each other in optimal terrain (ignoring the hills around them) and the winning side did not pursuit the enemy because a won battle usually meant a won war.
That changed over time; skirmishers were introduced. Javelineers (Peltasts from Trace), Bowmen (Cretans) and slingers (from Rhodes) became more important and harassed and exhausted the enemy lines before the clash as well as contributing to a pursuit. These lightly armed skirmishers (a mix of missile and light infantry) were elusive. They were more mobile than the heavy infantry (especially as the latter kept its formation) and not threatened much by cavalry (because horses were rare in greece - only Thessaloniki had much light cavalry).
The late Hellenic army of Alexander the Great's fame was built on a holding phalanx with extra-long lances and a heavy (shock) cavalry for the decisive breakthrough charge (typically aimed at the enemy army leader). This model withered down to a defensively strong but also offensively cumbersome phalanx with little cavalry support as the Macedonian successors of Alexander were unable to afford enough cavalry.
Rome went another path; it began with a graded infantry force with little cavalry and turned towards an army built with excellent heavy infantry supported by mercenaries. That model was fine, but was again given up late in the empire in favour of a less disciplined force with a greater share of heavy cavalry. The conditions had changed over time.
The Northern (Germanic) tribes had an emphasis on light infantry which got employed in a heavy infantry (shock infantry for battle) function, with predictably little success for centuries.
This model withered away in favour of less, but better armed and trained fighters after the Western Roman Empire's end. These new armies of the feudal societies moved towards small all-heavy (shock) cavalry forces (the knight armies).
The pendulum swung back to wards heavy infantry during the 13th to 15th century with another rise of lance-armed infantry (a Swiss reinvention). A revival of the bow happened late in that period with the zenith of bowmen in Europe; the English longbowmen. The quality of their bows was quite mediocre (the Turkish bows were much, much better), but their chosen and highly skilled users managed to exploit defects of the then-dominant heavy cavalry armies.
The combination of heavy infantry with lances and missileers with strong longbows sufficed to push cavalry back into a secondary role next to infantry.
Most European wars from the 16th to 20th century were dominated by heavy infantry of some sort, with notable exceptions on the Balkans (the wars against the Turks that required much light cavalry as well as light infantry) and the huge countries of Eastern Europe (much cavalry).
Firearms (both artillery and man-portable weapons) transformed European warfare to some degree, but their breakthrough came with the bayonet revolution of the mid-17th century. The bayonet gave the musket a dual role as a ranged weapon and as a lance. Pikes and lances had initially been necessary additions to muskets/arquebus because of their repulsion value against cavalry shock attacks. At about 1660 every infantryman was to be armed with a firearm plus melee and even anti-cavalry capability.
Heavy infantry and missile infantry had merged to a new type of heavy infantry (the line infantry) and later on light infantry and missile troops merged into a new type of light infantry (rifle infantry).
The dedicated missile infantry role was kind of taken over by artillery, which added a field artillery role to its siege role by producing sufficiently mobile gun designs.
That model lasted till after the Napoleonic Wars, although heavy infantry became able to fight with less discipline in addition to disciplined formations. Social and political changes of the French Revolution and the rise of nationalism had allowed for that change.
The next revolution came with the Minié ball (which finally made muzzle-loaded rifles practical for all infantry). The Minié ball reigned just a few years until the breech-loaded rifle was finally mature and ready for general use. Both together sealed the fate of horse cavalry as important battlefield factor - both the heavy and the light one.
Heavy infantry was still used with old tactics (despite having light infantry potential as well due to their rifles), and the slaughter was impressive.
The First World War finally helped to press some of the light infantry mindset into the heavy infantry, which was still the dominant branch for line-of-sight combat during WW2.
Early Word War Two demonstrated the return of the heavy (shock) cavalry principle of sorts - the internal combustion engine had replaced the muscles of horses. The wealth of nations after the recovery of the late 40's and the 50's allowed for national armies that focused on this new, most powerful heavy cavalry. The result seems to have been similar to the medieval result: Small forces of very powerful heavy cavalry with a considerable train - and a weak infantry.
The remainder of the heavy infantry (infused with just a few light infantry traits) has recently been pitched against the light infantry mustered by less developed countries and was found wanting; light infantry is still pretty elusive. The ringing alarm bell was heard and it's a question of problem pressure whether the recent experiences will lead to an increased emphasis on own light infantry or not.
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Now what's the point of this redux of oriental and occidental military history?
Simple: I wanted to point out that there's more than just our present structure. Most importantly, we seem to neglect the light cavalry pattern today. The only modern equivalent are our weak and neglected armoured reconnaissance forces. The present small wars-driven interest in light infantry is unlikely to help us to regain the advantages that light cavalry has to offer.
Light cavalry showed its full potential in the ancient Parthian light cavalry that faced the infantry-centric Roman armies.
The Romans were superior in melee battles and sieges, but their problems were quite insurmountable every time they invaded Parthia. The enemy light cavalry (armed with composite bows) simply bypassed the Roman main force and attempted to cut off the supply lines. Supply convoys had to be guarded heavily. The Romans tried to use an economies of scale approach with few very large convoys, but even more than one entire legion plus mercenary troops was at times not enough to prevent the complete destruction of an essential convoy.
Now imagine that we would revolutionize our armoured reconnaissance further and turn it into light cavalry, with much greater importance and much greater capabilities than today's armoured recce. Such an approach could be a mightily powerful answer to the challenge of low force density (geography stayed the same, but forces shrunk). Opposing heavy forces would be unable to defeat the more elusive light cavalry, be cut off, threatened all the time from all directions - and would be in a terrible situation if engaged by heavy opposition with great momentum.
In fact, I've been researching into this direction for a while and the many advantages of the concept are overwhelming. The crucial question is of course whether the force density in the theater is indeed low enough to allow for infiltration and exfiltration - light cavalry needs non-linear warfare to excel in its core roles of reconnaissance, counterreconnaissance, skirmishing, raiding, escorting and coup de mains.