I know that breast plates would not have stopped musket fire, but why didn't British soldiers ( for example ) issue breast plates from the 1600's - late 1800's? Most fighting happened hand to hand with bayonets. Couldn't these have been used to protect from melee? And during British conquest of more tribal regions that still fielded bow and arrow and relied heavily on melee weaponry?
Edit: Grammar and spelling
Armour of various types remained in use in European armies long after the introduction of firearms, but was for the most part restricted to cavalry. The breast plate or cuirass was the most commonly used type of armour worn by European cavalry from the early modern period through to the beginning of the 20th Century, and even lent its name to the term cuirassier, a type of heavy cavalry prominent in the period. Use of armour for cavalry in this period was intermittent, falling in and out of fashion periodically in the 18th and 19th Centuries. It was primarily used by heavy cavalry which engaged in shock tactics, as it was most useful in close combat as you suggest.
In this period infantry generally went without armour, as many foot soldiers had throughout history. There are numerous factors contributing to this of which its relative ineffectiveness against firearms it but one. Cost and availability were significant factors, and as armies grew larger and larger throughout the period these problems were only exacerbated. However, chief among the detriments of equipping infantry with armour from a military perspective was its weight. Any added protection it may have provided would have come at the cost of limiting soldiers' battlefield mobility and the amount of kit and supplies they could carry on the march. As European warfare in the 18th and 19th Centuries emphasized prolonged maneuvering for advantage logistics was always a major concern, and any unnecessary weight that could be ejected was.
In colonial warfare concerns of climate also played a role in the decline of armour, with even cavalry regiments in British India for the most part forgoing it despite its continued use by some local Indian cavalry, notably and effectively in the Sikh Dal Khalsa under Ranjit Singh. It also goes without saying that outside of Europe logistical concerns were an even greater factor, especially in tropical areas and interiors lacking developed road infrastructure similar to that present in Europe at the time.
By the 19th Century advances in firearms technology had made armour even less effective against firearms and therefore even less desirable, although effective - and ineffective - 'home-made' breastplates were used by individual soldiers as late as the American Civil War.