Early modern warfare
A man by the name of Konstantin Mihailović was captured by the Turks in 1455 and would eventually write a memoir about his time with the Ottoman Empire's Janissary units. His account would be considered flawed because of the translations from Serbian to Czech and Polish. There is no original text from his memoir and only translations are left to work from, and those have far fetched ideas of what the Janissaries were doing during the time. He was recaptured in 1463 by Hungarian troops and eventually wrote the memoir after he became a Christian again. His memoir is an important piece of history, but scholars and historians have widely debated the authentic nature of his stories and doubt the consistency of his tales.
The Ottoman Empire was one of the first states to put gunpowder weapons into widespread use. The famous Janissary corps of the Ottoman army began using matchlock muskets as early as the 1440s. The army of Mehmed the Conqueror, which conquered Constantinople in 1453, included both artillery and foot soldiers armed with gunpowder weapons. The Ottomans brought to the siege sixty-nine guns in fifteen separate batteries and trained them at the walls of the city. The barrage of Ottoman cannon fire lasted forty days, and they are estimated to have fired 19,320 times.

16th century: The 16th century saw the first widespread use of the matchlock musket as a decisive weapon on the battlefield with the Turks becoming leaders in this regard. The first of these campaigns was the campaign against the Persians in 1514 under Yavuz Sultan Selim, or Selim the Grim. Armed with gunpowder weapons, his army defeated the Persians at the Battle of Chaldiran. After his victory over the Safavids, Selim turned his attention towards the Mamluk dynasty in Egypt. The decisive battle of his campaign against the Mamluks, and the battle which highlighted the importance of the musket in the Ottoman military, was the Battle of Raydaniyah, fought in 1517. There, Selim outflanked the entrenched Mamluk artillery, and attacked the Mamluk forces with his Janissaries. The Janissaries, armed with firearms, destroyed the Mamluk army, armed mostly with traditional swords and javelins.
Reference was made by João de Barros to a sea battle outside Jiddah, in 1517, between Portuguese and Ottoman vessels. The Muslim force under Salman Reis had "three or four basilisks firing balls of thirty palms in circumference". This was estimated to be a cannon of about 90 inch bore "firing cut stone balls of approximately 1,000 pounds (453 kg)".
After the death of Selim, he was succeeded by his son Suleiman the Magnificent. During his reign, gunpowder weapons continued to be used effectively. One important example is the Battle of Mohács in 1526. During this battle, Ottoman artillery, and Janissaries armed with muskets, were able to cut down charging Hungarian cavalry.

17th century: Although the cannon and musket were employed by the Ottomans long beforehand, by the 17th century they witnessed how ineffective the traditional cavalry charges were in the face of concentrated musket-fire volleys. In a report given by an Ottoman general in 1602, he confessed that the army was in a distressed position due to the emphasis in European forces for musket-wielding infantry, while the Ottomans relied heavily on cavalry. Thereafter it was suggested that the Janissaries, who were already trained and equipped with muskets, become more heavily involved in the imperial army while led by their agha.
By the middle of the 17th century, the continued reliance of the Ottomans on over-heavy ordnance had been made out by European officers as a liability. Raimondo Montecuccoli, the Habsburg commander who defeated the Ottomans at Battle of Saint Gotthard commented on Ottoman cannon:

This enormous artillery produces great damage when it hits, but it is awkward to move and it requires too much time to reload and site. Furthermore, it consumes a great amount of powder, besides cracking and breaking the wheels and the carriages and even the ramparts on which it is placed ... our artillery is more handy and more efficient and here resides our advantage over the cannon of the Turks.

Vietnam: Western matchlock arquebuses were imported into Vietnam during the early 16th century. The raging and lengthy wars between Le and Mac dynasties, and later Trinh and Nguyen clans invoked an arm race between the opposing factions. Gunnery and marksmanship rapidly spread across the country and soon Vietnamese musketeers became famous within Asia as masters of firearms.

See also: Gunpowder magazine
Kabinettskriege
Battle of Caishi
Battle of Tangdao
Technology of the Song dynasty
Early modern period

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External links: Military Science in Western Europe in the 16th Century. Prologue: The Nature of Armies in the 16th Century (PDF).
From Gunpowder to World Domination