The Chinese made the first firearms, cannons and explosive grenades. The Europeans just improved upon them in the 16th-19th centuries.
The earliest gunpowder weapons we know of in world history were used in the 11th century by the Song dynasty. The first kind of "firearm" was literally a spear that also doubled as a flamethrower, with a tube of gunpowder tied close to the blade that could be ignited when the enemy approached. It was called the "firespear" (火枪 huoqiang), and that's why guns are still called qiang 枪 in China today, the same word as "spear". In 1259 in the Southern Song, the first true gun was also invented - a bamboo tube firing a single pellet that was called the 突火枪 tuhuoqiang ("fire-shooting spear"). The Song also had a very wide variety of explosive bombs and mines that could be thrown, laid in the ground, or launched from trebuchets.
The oldest extant cannon that we have is a bronze cannon from the Yuan dynasty, with an inscription dated 1332. It is 35.3cm long, with a calibre of 10.5cm and a weight of 6.94kg. The inscription also tells us that it was cannon number 300 in its frontier guard unit, showing that such cannons were manufactured and deployed in large numbers. The muzzle of the cannon is flared out in a bowl shape, which is characteristic of cannons from the late Yuan to the early Ming (see the pictures at
http://202.102.202.102/qt/new_page_450.htmhttp://www.yzls.net/zglstp/Zs084362.jpg and
http://www.yzls.net/zglstp/Zs093400.jpg )
Until recently, the oldest extant metal handgun was a Yuan dynasty bronze handgun (火铳 huochong) with an inscription dated 1351. It is 43.5cm long (longer than the cannon!), including a 14.6cm long stock, with a calibre of 3cm. The range of the gun is estimated to be about 180m. Because of its length, it was often operated on a stand by two men, with one man steadying the stand while the other ignited the fuse leading to the gunpowder chamber.
However, in June this year, a collector in Ningxia province revealed a handgun with an inscription dated 1271, during the reign of Khubilai Khan and five years before the Mongol conquest of the Southern Song. It is 34.6cm long, with a calibre of 2.6cm, and shaped like an elongated vase. The report (in Chinese) is here:
http://tech.enorth.com.cn/system/2004/06/09/000799394.shtmlDuring the civil wars and rebellions at the end of the Yuan dynasty, trebuchets and cannons were used together because of the relatively small calibre of cannons, which still made them less effective against city walls. In the Ming dynasty, large iron cannons began to be produced, while wooden and bamboo cannons could also be improvised. The uses of cannons broadened from siege warfare and city defence to also include naval warfare and field deployment. Wheeled carriages for cannons also began to be used for the first time.
During the Ming dynasty, as GZ has mentioned, large humbers of cannon were also imported from Europe, and were known as 佛朗机 folangji ("Frankish Machines") and 红夷炮 hongyipao ("Red-haired Barbarian Cannons"). Most of these were from Portugal and Holland, and had superior range, calibre and durability compared to Chinese cannons. But the Chinese quickly learned how to copy these cannons, and began making their own, although they continued to call them "Frankish Machines" and "Red-haired Barbarian Cannons". These types of cannon were the main artillery of Chinese armies until well into the Qing dynasty.
During the Ming dynasty, rocket launchers were also invented. The earliest rockets were first used in the Southern Song, and were called fire-arrows (huojian 火箭), and that remains the Chinese term for rockets (even the ones that land on the moon). These rockets were, like the fire-spears, arrows with tubes of gunpowder tied to them to allow them to fly on their own power. Throughout the Ming dynasty, launchers with large numbers of these rockets were used in field combat, but by the early Qing, with the introduction of more efficient handguns (arquebuses), the rockets became largely redundant. A picture of a fire-arrow rocket:
http://www.yzls.net/zglstp/Zs075324.jpg