Cavalry
The cavalry of Goguryeo, one of the Three Kingdoms of Korea, were called Gaemamusa (개마무사, 鎧馬武士), and were renowned as a fearsome heavy cavalry force. King Gwanggaeto the Great often led expeditions into the Baekje, Gaya confederacy, Buyeo, Later Yan and against Japanese invaders with his cavalry.

In the 12th century, Jurchen tribes began to violate the Goryeo–Jurchen borders, and eventually invaded Goryeo Korea. After experiencing invasion by the Jurchen, Korean general Yun Kwan realized that Goryeo lacked efficient cavalry units. He reorganized the Goryeo military into a professional army that would contain decent and well-trained cavalry units. In 1107, the Jurchen were ultimately defeated, and surrendered to Yun Kwan. To mark the victory, General Yun built nine fortresses to the northeast of the Goryeo–Jurchen borders (동북 9성, 東北 九城).

Japan: The ancient Japanese of the Kofun period also adopted cavalry and equine culture by the 5th century AD. The emergence of the samurai aristocracy led to the development of armoured horse archers, themselves to develop into charging lancer cavalry as gunpowder weapons rendered bows obsolete.  Japanese cavalry was largely made up of landowners who would be upon a horse to better survey the troops they were called upon to bring to an engagement, rather than traditional mounted warfare seen in other cultures with massed cavalry units.
An example is Yabusame (流鏑馬), a type of mounted archery in traditional Japanese archery. An archer on a running horse shoots three special "turnip-headed" arrows successively at three wooden targets.
This style of archery has its origins at the beginning of the Kamakura period. Minamoto no Yoritomo became alarmed at the lack of archery skills his samurai had. He organized yabusame as a form of practice.
Currently, the best places to see yabusame performed are at the Tsurugaoka Hachiman-gū in Kamakura and Shimogamo Shrine in Kyoto (during Aoi Matsuri in early May). It is also performed in Samukawa and on the beach at Zushi, as well as other locations.
Kasagake or Kasakake (笠懸, かさがけ lit. "hat shooting") is a type of Japanese mounted archery. In contrast to yabusame, the types of targets are various and the archer shoots without stopping the horse. While yabusame has been played as a part of formal ceremonies, kasagake has developed as a game or practice of martial arts, focusing on technical elements of horse archery.

South Asia: 

Indian subcontinent: In the Indian subcontinent, cavalry played a major role from the Gupta dynasty (320–600) period onwards. India has also the oldest evidence for the introduction of toe-stirrups.
Indian literature contains numerous references to the mounted warriors of the Central Asian horse nomads, notably the Sakas, Kambojas, Yavanas, Pahlavas and Paradas. Numerous Puranic texts refer to a conflict in ancient India (16th century BC) in which the horsemen of five nations, called the "Five Hordes" (pañca.ganan) or Kṣatriya hordes (Kṣatriya ganah), attacked and captured the state of Ayudhya by dethroning its Vedic King Bahu

The Mahabharata, Ramayana, numerous Puranas and some foreign sources attest that the Kamboja cavalry frequently played role in ancient wars. V. R. Ramachandra Dikshitar writes: "Both the Puranas and the epics agree that the horses of the Sindhu and Kamboja regions were of the finest breed, and that the services of the Kambojas as cavalry troopers were utilised in ancient wars". J.A.O.S. writes: "Most famous horses are said to come either from Sindhu or Kamboja; of the latter (i.e. the Kamboja), the Indian epic Mahabharata speaks among the finest horsemen".

The Mahabharata speaks of the esteemed cavalry of the Kambojas, Sakas, Yavanas and Tusharas, all of whom had participated in the Kurukshetra war under the supreme command of Kamboja ruler Sudakshin Kamboj.
Mahabharata and Vishnudharmottara Purana pay especial attention to the Kambojas, Yavansa, Gandharas etc. being ashva.yuddha.kushalah (expert cavalrymen). In the Mahabharata war, the Kamboja cavalry along with that of the Sakas, Yavanas is reported to have been enlisted by the Kuru king Duryodhana of Hastinapura.
Herodotus (c. 484 – c. 425 BC) attests that the Gandarian mercenaries (i.e. Gandharans/Kambojans of Gandari Strapy of Achaemenids) from the 20th strapy of the Achaemenids were recruited in the army of emperor Xerxes I (486–465 BC), which he led against the Hellas. Similarly, the men of the Mountain Land  from north of Kabul-River equivalent to medieval Kohistan (Pakistan), figure in the army of Darius III against Alexander at Arbela, providing a cavalry force and 15 elephants. This obviously refers to Kamboja cavalry south of Hindukush.
The Kambojas were famous for their horses, as well as cavalrymen (asva-yuddha-Kushalah). On account of their supreme position in horse (Ashva) culture, they were also popularly known as Ashvakas, i.e. the "horsemen" and their land was known as "Home of Horses". They are the Assakenoi and Aspasioi of the Classical writings, and the Ashvakayanas and Ashvayanas in Pāṇini's Ashtadhyayi. The Assakenoi had faced Alexander with 30,000 infantry, 20,000 cavalry and 30 war elephants. Scholars have identified the Assakenoi and Aspasioi clans of Kunar and Swat valleys as a section of the Kambojas. These hardy tribes had offered stubborn resistance to Alexander (c. 326 BC) during latter's campaign of the Kabul, Kunar and Swat valleys and had even extracted the praise of the Alexander's historians. These highlanders, designated as "parvatiya Ayudhajivinah" in Pāṇini's Astadhyayi, were rebellious, fiercely independent and freedom-loving cavalrymen who never easily yielded to any overlord.
The Sanskrit drama Mudra-rakashas by Visakha Dutta and the Jaina work Parishishtaparvan refer to Chandragupta's (c. 320 BC – c. 298 BC) alliance with Himalayan king Parvataka. The Himalayan alliance gave Chandragupta a formidable composite army made up of the cavalry forces of the Shakas, Yavanas, Kambojas, Kiratas, Parasikas and Bahlikas as attested by Mudra-Rakashas (Mudra-Rakshasa 2). These hordes had helped Chandragupta Maurya defeat the ruler of Magadha and placed Chandragupta on the throne, thus laying the foundations of Mauryan dynasty in Northern India.
The cavalry of Hunas and the Kambojas is also attested in the Raghu Vamsa epic poem of Sanskrit poet Kalidasa. Raghu of Kalidasa is believed to be Chandragupta II (Vikaramaditya) (375–413/15 AD), of the well-known Gupta dynasty.
As late as the mediaeval era, the Kamboja cavalry had also formed part of the Gurjara-Pratihara armed forces from the eighth to the 10th centuries AD. They had come to Bengal with the Pratiharas when the latter conquered part of the province.
Ancient Kambojas organised military sanghas and shrenis (corporations) to manage their political and military affairs, as Arthashastra of Kautiliya as well as the Mahabharata record. They are described as Ayuddha-jivi or Shastr-opajivis (nations-in-arms), which also means that the Kamboja cavalry offered its military services to other nations as well. There are numerous references to Kambojas having been requisitioned as cavalry troopers in ancient wars by outside nations.

Mughal Empire: The Mughal armies (lashkar) were primarily a cavalry force. The elite corps were the ahadi who provided direct service to the Emperor and acted as guard cavalry. Supplementary cavalry or dakhilis were recruited, equipped and paid by the central state. This was in contrast to the tabinan horsemen who were the followers of individual noblemen. Their training and equipment varied widely but they made up the backbone of the Mughal cavalry. Finally there were tribal irregulars led by and loyal to tributary chiefs.