Mounted archer
Basic features: Since using a bow requires the rider to let go of the reins with both hands, horse archers need superb equestrian skills if they are to shoot on the move. The natives of large grassland areas used horse archery for hunting, for protecting their herds, and for war. Horse archery was for many groups a basic survival skill, and additionally made each able-bodied man, at need, a highly mobile warrior. The buffalo hunts of the North American prairies may be the best-recorded examples of bowhunting by horse archers.
In battle, light horse archers were typically skirmishers, lightly armed missile troops capable of moving swiftly to avoid close combat or to deliver a rapid blow to the flanks or rear of the foe. Captain Robert G. Carter described the experience of facing Quanah Parker's forces: "an irregular line of swirling warriors, all rapidly moving in right and left hand circles.. while advancing, to the right or left, and as rapidly concentrating... in the centre... and their falling back in the same manner...all was most puzzling to our... veterans who had never witnessed such tactical maneuvers, or such a flexible line of skirmishers"
In the tactic of the Parthian shot the rider would retreat from the enemy while turning his upper body and shooting backward. Due to the superior speed of mounted archers, troops under attack from horse archers were unable to respond to the threat if they did not have ranged weapons of their own. Constant harassment would result in casualties, morale drop and disruption of the formation. Any attempts to charge the archers would also slow the entire army down.
An example of these tactics comes from an attack on Comanche horse archers by a group of Texas Rangers, who were saved by their muzzle-loading firearms and by a convenient terrain feature. Fifty Rangers armed with guns met about 20 Comanche hunters who were hunting buffalo and attacked them. The Comanches fled, easily keeping clear of the Rangers, for several miles across the open prairie. They led the Rangers into a stronger force of two hundred. The Rangers immediately retreated, only to discover they had committed a classic error in fighting mounted archers: the Comanches pursued in turn, able to shoot what seemed like clouds of arrows. The Rangers found a ravine where they could shoot at the Comanche from cover. The horse archers did not charge but kept the Rangers under siege until seven of them were dead or dying, whereupon the Rangers retreated but claimed victory.

Heavy horse archers: Horse archers may be either light, such as Scythian, Hun, Parthian, Cuman, or Pecheneg horsemen, or heavy, such as Byzantine kavallarioi, Turkish timariots, Russian druzhina and Japanese samurai. Heavy horse archers typically fought as formed units. Instead of harassing without ever making contact, they shot in volleys, weakening the enemy before they charged. In addition to bows, they often also carried close combat weapons, such as lances or spears. Some nations, like medieval Mongols, Hungarians and Cumans, fielded both light and heavy horse archers. In some armies, such as those of the Parthians, Palmyrans, and the Teutonic Order of Knights, the mounted troops consisted of both super-heavy troops (cataphracts and knights) without bows, and light horse archers.

Appearance in history: Horse archery first developed during the Iron Age, gradually replacing the Bronze Age chariot.
The earliest depictions are found in the artwork of the Neo-Assyrian Empire of about the 9th century BC and reflect the incursions of the early Iranian peoples.
Early horse archery, depicted on the Assyrian carvings, involved two riders, one controlling both horses while the second shot. Heavy horse archers first appeared in the Assyrian army in the 7th century BC after abandoning chariot warfare and formed a link between light skirmishing cavalrymen and heavy cataphract cavalry. The heavy horse archers usually had mail or lamellar armor and helmets, and sometimes even their horses were armored.
Mounted archery was prevalent in the cavalry tactics of Meroitic and post-Meroitic Nubia.
Skirmishing requires vast areas of free space to run, maneuver, and flee, and if the terrain is close, light horse archers can be charged and defeated easily. Light horse archers are also very vulnerable to foot archers and crossbowmen, who are smaller targets and can outshoot horsemen. Large armies very seldom relied solely on skirmishing horse archers, but there are many examples of victories in which horse archers played a leading part. The Roman general Crassus led a large army, with inadequate cavalry and missile troops, to catastrophe against Parthian horse archers and cataphracts at the Battle of Carrhae. The Persian king Darius the Great led a campaign against the mounted Scythians, who refused to engage in pitched battle; Darius conquered and occupied land but lost enough troops and supplies that he was compelled to withdraw. Darius, however, kept the lands he had conquered.
According to the Greek historian Herodotus, the Persian general Mardonius used horse archers to attack and harass his opponents during the Battle of Plataea, which was won by the Greeks. Philip of Macedon scored an epic victory against the Scythians residing north of the Danube, killing their king, Ateas, and causing their kingdom to fall apart thereafter. Alexander the Great defeated Scythians/Sakas in 329 BC at the Battle of Jaxartes, at the Syr Darya river. Later on, Alexander himself used mounted archers recruited among the Scythians and Dahae, during the Greek invasion of India.
The Roman Empire and its military also had extensive use of horse archers after their conflict with eastern armies that relied heavily on mounted archery in the 1st century BC. They had regiments such as the Equites Sagittarii, who acted as Rome's horse archers in combat. The Crusaders used conscripted cavalry and horse archers known as the Turcopole, made up of mostly Greek and Turks.
Heavy horse archers, instead of skirmishing and hit-and-run tactics, formed in disciplined formations and units, sometimes intermixed with lancers as in Byzantine and Turkish armies, and shot as volleys instead of shooting as individuals. The usual tactic was to first shoot five or six volleys at the enemy to weaken him and to disorganize them, and then charge. Heavy horse archers often carried spears or lances for close combat or formed mixed units with lancers. The Mongol armies and others included both heavy and light horse archers.
Heavy horse archers could usually outshoot their light counterparts, and because of the armor they wore, could better withstand return fire. The Russian druzhina cavalry developed as a countermeasure to the Tatar light troops. Likewise, the Turkish timariot and qapikulu were often as heavily armored as Western knights and could match the Hungarian, Albanian, and Mongol horse archers.

Vietnam's mounted archers were first recorded in the 11th century. In 1017, Emperor Lý Công Uẩn of Đại Việt opened the Xa Dinh (archery school) in southern Hanoi and ordered all children of noblemen and mandarins to be trained in mounted archery. During the reign of Lý Thánh Tông, the royal guards had 20 horse archer teams, combined into 5 companies named Kỵ Xạ, Du Nỗ, Tráng Nỗ, Kính Nỗ, and Thần Tý, comprising about 2,000 skillful horse archers. They later effectively participated in the Invasion of Song China (1075 – 1076) and caused heavy casualties to the Song army. The Ly Dynasty's horse archers also fought against Champa (1069) and the Khmer Empire (1125–1130) which both were victories for Đại Việt. Later, following the decline of the Lý dynasty, most horse archer teams were disbanded.
German and Scandinavian medieval armies made extensive use of mounted crossbowmen. They would act not only as scouts and skirmishers but also protect the flanks of the knights and infantry, chasing away enemy light cavalry. When the battle was fully engaged, they would charge at the enemy flank, shoot a single devastating volley at point-blank range and then attack the enemy with swords, without reloading. In some instances, mounted crossbowmen could also reload and fire continuously on horseback if they used specific "weaker" crossbows that could be reloaded easily, as mentioned in the 13th-century Norwegian educational text Konungs skuggsjá. The invention of spanning mechanisms such as the goat's foot lever and the cranequin allowed mounted crossbowmen to reload and fire heavy crossbows on horseback.

Decline: Horse archery was usually ineffective against massed foot archery. The foot archers or crossbowmen could outshoot horse archers and a man alone is a smaller target than a man and a horse. The Crusaders countered the Turkoman horse archery with their crossbowmen, and Genoese crossbowmen were favoured mercenaries in both Mamluk and Mongol armies. Likewise the Chinese armies consisted of massed crossbowmen to counter the nomad armies.