/u/WARitter's answer, linked below, is excellent, but I think it's also worth establishing some broader context. His answer is primarily addressing the impact firearms had on armour once viable handheld firearms were invented. This last bit is kind of important, because gunpowder weaponry didn’t revolutionize warfare in the immediate way many people imagine. If you want to know the impact the introduction of gunpowder had on armour, the answer is that it didn’t have any effect at all really. There’s a couple of key reasons for this.

Firstly, we should go over the timeline of early gunpowder weaponry. The exact date of gunpowder’s invention is still a subject of some debate. General consensus puts its invention in China, from which it is assumed to have spread through the Middle East and eventually reached Europe. We get our first definite mentions of gunpowder in Europe in the late 13th century. Famed scholar and natural philosopher Roger Bacon (c.1219-c.1292) is the first European to record gunpowder, while the oldest surviving European recipe for gunpowder comes to us from the Liber Ignium of Marcus Graecus (probably not his real name) which has been generally dated to c. 1300. Gunpowder as it is described in these texts is still pretty much a novelty item, Roger Bacon pretty much just describes modern firecrackers in his accounts, and it took a little while for its military implications to become clear.

The first solid evidence we have for gunpowder being used in guns comes in 1326 and courtesy of Walter de Milemete. Milemete was an English scholar who was commissioned to write a book on young prince Edward (later Edward III). In this manuscript he included a somewhat famous picture. This image, along with a nearly identical image of about the same time in a copy of De Secretis Secretorum possibly also by Walter, is the earliest known depiction of a firearm (in the West anyway, the area I’m comfortable commenting on). It seems likely that gunpowder weaponry was invented sometime before this image was drawn, but exactly how long before we cannot determine without more evidence. Not too long after this guns begin appearing in textual sources, with several mentions in English documentation around the mid-14th century. There’s even some evidence to suggest that they were present at the Battle of Crecy (1346), but they don’t seem to have made much of an impact there.

While there were some passing mentions of handheld firearms during this period, the early stages of gunpowder history were almost exclusively centred on artillery. Despite their appearance at Crecy, field artillery wasn’t much of a thing in the Middle Ages (there’s a lot of reasons for this), which limited early gunpowder artillery to a primarily siege based role. Their virtually non-existent impact on the medieval battlefield meant that early guns had no demonstrable impact on medieval armour. Early guns were rendered even more impractical due to the extreme costs of gunpowder. While manufacturing guns was reasonably affordable, and both charcoal and sulphur weren’t too expensive, the cost of saltpetre was extraordinary. It took decades for Europeans to invent a cost-effective way to manufacture saltpetre, and until that could be done guns were pretty much restricted to being a novelty weapon.

It wasn’t until the fifteenth century, nearly a century after gunpowder weaponry was first invented, that affordable, effective, and reliable guns began to see wider use in European warfare. Even then, they remained relatively niche weapons until at least the middle of the century. The fourteenth century saw significant innovation (and numerous failed experiments) in developing effective artillery and guns, but it took all of this work (as well as several advances in gunpowder manufacturing and storage) for guns to begin to make their impact on medieval warfare.

None of this is intended to contradict what /u/WARitter said in his post already linked in this thread (which is an excellent answer, and possibly more appropriate to what you’re interested in learning). It is instead to point out that there is a solid century’s worth of gunpowder history before we reach the point he is talking about.

Sources: Blair, Claude, 'Early Firearms', Claude Blair (ed.), Pollard's History of Firearms, (Feltham, 1983). p. 25-32.

Davies, Jonathan, Gunpowder Artillery 1267-1603, (Bristol, 2003).

DeVries, Kelly, 'Gunpowder and Early Gunpowder Weapons', Kelly DeVries (ed.), Guns and Men in Medieval Europe, 1200-1500, (Aldershot, 2002). pp. 121-135.

Hall, Bert S., 'The Corning of Gunpowder and the Development of Firearms in the Renaissance', Brenda Buchanan (ed.), Gunpowder: the History of an International Technology, (Bath, 1996). pp. 87-120.

Rimer, Graeme, 'Early Handguns', Royal Armouries Yearbook, Vol. 1 (1996). p. 73-78.

Tout, T.F., ‘Firearms in England in the Fourteenth Century’, The English Historical Review, Vol. 26 No. 104 (1911). pp. 666-702.

Zaky, A. Rahman, 'Gunpowder and Arab Firearms in the Middle Ages', Gladius, Vol. 6 (1967). pp. 45-58.

In addition to the answer that u/tiredstars linked above, you may be interested in some other answers I have provided in the past:

• AskHistorians Podcast 083 - The European Armoring Guilds and People 1300-1600 - this podcast episode discusses the history of plate armour in the 16th century and the decline of the armouring industry.

• A Brief History of Plate Armour - this provides an overview of plate armour's adoption, apogee in the late 15th/early 16th century and eventual decline in the later 16th century.

• How effective was plate armor against musketballs?

• Would a 17th Century breastplate have stopped a pistol/musket ball?

Take a look at the response here, which is probably the best summary on the sub of the introduction of firearms and its impact on armour. /u/WARitter is the resident expect, but I may be able to answer follow-up questions, or point you to somewhere else they've been answered.

For comparing styles, try looking at the Royal Armouries site. It allows you to filter down by type of object, date and place (which I think means place of manufacture).