Glass, in the form of naturally occurring volcanic glass, obsidian, was used in warfare, for arrow points, knives, and even as blades on wooden-bodied clubs (e.g., the Aztec macuahuitl). Obsidian is one of the best naturally-occurring materials for making traditional stone blades - very sharp blades are possible (but also brittle, which is shared by other stone blades). Obsidian was often traded over long distances, as a consequence of its desirability and scarceness. For some reading on the ancient Mediterranean obsidian trade, see Dixon, J., Cann, J., & Renfrew, C, (1968), "Obsidian and the Origins of Trade", Scientific American, 218(3), 38-47.

I don't know of any ancient or medieval examples of bladed stone tools/weapons being made of artificial glass (stone arrowheads (and bone, and horn, and wood/bamboo) were used long into the Iron Age in some places, as cheaper and more available alternatives to iron, but artificial glass was hardly a cheap alternative to iron compared to stone, wood, h horn, and bone). In more modern times, with colonists from industrial nations living alongside native peoples who still used stone tools/weapons, glass (e.g., bottle bottoms) was used for making blades, and hobbyist knappers continue making such blades today. There is also some use of flaked glass blades in modern microsurgery.

Bronze and iron arrowheads (and spearheads, and knives, etc.) are typically not as sharp as stone/glass heads, but are much tougher. While toughness is very important for knives, spears, and swords, it is less important for arrowheads, since while brittle arrowheads can make the arrow a single-use weapon, this isn't necessarily a bad thing, since you don't want the enemy shooting your own arrows back at you. However, toughness is important for penetrating armour - if the head breaks on impact, the arrow isn't going to penetrate. Increasing use of armour made metal (bronze and iron) arrowheads relatively better.

While glass is an excellent material for making stone blades and points, various other types of stone are also good materials, and one side using glass/obsidian arrowheads while the other side uses flint (or bone, or horn, or wood) will not be a battle-winning advantage.

I recall hearing about glass and clay shards being used in rudimentary grenades during the crusades but is that even true?

Early grenades often used ceramic containers. E.g., https://en.wikipedia.org/wiki/File:Handgrenades_Ingolstadt.jpg for a 17th century example. Before explosive grenades, such containers were used for firebombs; this usage goes back to early Medieval times, if not earlier. By late Medieval times, glass was being used for grenades - see, e.g., Triantafyllidis, P, (2016), "War in Medieval Mytilene, Lesbos, Greece: Glass Grenades of the 14th and 15th Centuries", Journal of Glass Studies, 58, 296-300. (Another early grenade material was cast iron, used in Song China, and later, elsewhere.)

Moving past Medieval times, glass found much important use in warfare, in the form of optical instruments. Telescopes, optical rangefinders, periscopes, cameras, etc. The telescope saw such use in the 17th century, and other optical instruments followed later.