Eastern Europe, despite utilizing somewhat comparable weaponry, was very distinct from the Western one both in army compositions and tactics. By 1500s all major Eastern players (Russia, Poland, Lithuania, Tatar Khanates, Livonian Confederation and Ottoman Empire) developed their own, quite distinct military arms, often influencing each other.

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Major trait shared by all the Eastern European countries of this period is the dominant role of cavalry. Being relatively scarclely populated (Russian Tsardom, according to opinions of different modern historians, possessed 2-4 millions people, roughly the same as Lithuania and slightly less than Poland and much less than, say, France's 16 millions during the same era; Crimean Khanate was even less than that with 0,5-1 million at max) and simultaneously larger than Western Europe, Eastern states couldn't field large infantry-focused armies and actually didn't have many reasons to do so anyway: long distances between inhabited lands and relative scarcity of strong defensive lines of castles meant it was the perfect ground for lightning fast raiding operations since horsemen were very fast in comparison to slow-marching infantry and could operate on plunder they gathered from enemy lands. Wars in Eastern Europe were wars of active maneuvers, extremely rare decisive field battles and lots of mutual raiding and scouting missions. Many conflicts in this era had participants from every side behaving in the similar manner: they would invade opposing territory, loot as many defenseless places as possible and fall back before enemy patrols could intercept them. Large-scale pitched battles were very undesirable since it was extremely hard to replenish troops (remember, fewer people also meant less money to spend) lost in engagement and wasn't as damaging to enemy economy (and supportive to your own) as taking their supplies and enslaving their peasantry to put to work or ransom later.

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Eastern European cavalry was very diverse in their looks, tactics and armament, coming in both light and heavy types, with the former predominating. Many countries still used illusive horse archers to great effect as they were fast, nimble, extremely effective in raids and punitive expeditions and able to lure away enemy forces or engage them from surprising direction. Since 16th century's firearms were already quite sophisticated it wasn't unheard of for these light horsemen to also take pistols and early carbines with them in case they would need superior firepower of the gunpowder weapon. These light skirmishers would often engage their enemies with carbines and bows at a distance and continuously rain fire and arrows upon them. Once the enemy breaks formation and tries to catch them, they would either disperse, evading pursuit, or encircle adversaries to finish them off with decisive charges from multiple sides.

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Russian Tsardom's light horsemen, called pomestnaya konniza ("local/feudal cavalry"), were feudal levies consisting of low-rank nobility and their servants, much like Medieval knights' retinue. Organized into different regiments, they were often mobilized from the provinces closest to the area of conflict and used in raiding actions on enemy territory. Konniza's armour was distinctly light, either chainmail or different types of brigantines, with horses usually being unarmoured. Close combat weaponry usually consisted out of sabres. bec-de-corbins, maces or axes with spears being relatively uncommon: Russian cavalry would often evade direct engagement with heavier types and retreat before being overrun (with Tatars being notable exception: 1555 battle of Slobodishi saw Russian cavalry breaking through nomadic ranks with cavalry charges since Tatars were sometimes even more lightly armed than konniza). You can get the general idea of pomestnaya konniza's looks from this picture (drawn by O. Fedorov).

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Roughly the same idea was also at play in Lithuania: called pospolitoe rushenie ("general mobilization"), it consisted of noblemen and their servants enlisted from different cities to form small temporary armies in order to either defend or raid enemy territory. Being on the heavier side, Poland (and, later, Polish-Lithuanian Commonwealth) actively used knights clad in full plate mail supported by rushenie or pancirni ("armoured") cossacks (those usually wore light chainmails and were skilled horse bowmen) to pin down enemy forces and crush them with decisive cavalry charge. Heavy knights of Poland would later incorporate firearms and change their armour for lighter versions, eventually transforming into hussars (picture by Polish painter Joseph Brandt)

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Horsemen constituted the main fighting core of Kazan, Crimean and Kalmyk Khanates, with first two being keen on figthing from the distance and the last one preferring to use masses of lancers. Tatars were incredibly skilled riders and, despite often having very light armour or having no protection at all, often emerged victorious by tricking their enemy to fight on unfavourable ground (such as battle of Sokal, 1519, where Tatar horsemen were able to evade and effectively harass Polish cavalry slowed down by terrain) or attacking them from the rear due to successful strategic maneuvering (battle of Oka against the Russians, 1521).

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Despite also utilizing large batallions of infantry in form of Janissaries, Ottomans often fielded large quantities of cavalry units called sipahi, armed with lances and bows. Their tactics were similar to other Eastern cavalry units: skirmishing actions, feigned retreat (so Janissaries could suddenly strike advancing enemies with firearms) and final charges in order to saw confusion among enemy ranks and chase down fleeing opponents.

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Livonian Confederation, de jure subordinate to the Holy Roman Empire, often had to deal with Polish, Lithuanian and Russian aggression. Since it didn't have any source of skilled horse riders, Confederates tried to make up with early versions of reitars, light cavalry armed with pistols and carbines, which could also dismount and turn into arquebusiers.