A quick history then about grenades, since I don't want to study anymore. Grenades have been around for a long time. Their predecessors were used by the post-Rome Byzantines, and the first major use of gunpowder grenades was in the 11th century by the Chinese, since the Chinese had gunpowder centuries before Europe or the Middle East. The first documentation we have of white people using grenades was in the late 15th century.

Jump ahead to Louis XIV, a straight up baller who should be read about by everyone. He made the grenadier a proper unit of the military, and chose the biggest (so they could throw the very heavy grenades), bravest (because getting close enough to throw a grenade is spooky) and meanest (because after the grenade throw melee combat followed) members of the infantry. Grenadiers threw grenades from well in front of musket range, and the grenades of the 17th-early 18th century were very heavy cricket balls, thrown like shot puts.

The grenade fell out of fashion in the 18th century. With the focus on discipline and order so crucial to line tactics, a shock weapon was less effective, and since armies were restructuring to allow for linear combat on a thinner, wider and more effective scale, getting in close long enough to throw heavy grenades was becoming less and less viable. Also remember that cannon really came into their own under Gustavus Adolphus (sorry Jan Zizka, you were way ahead of your time) in the 30 years war, and by the 18th century tactics and technology had caught up and advanced: canister shot did the same thing as grenades but better, safer and more reliably.

Horse grenadiers lasted slightly longer, but even they abandoned the grenade as tactics shifted away from it. Grenadiers were still an important part of infantry makeup. One company in the Napoleonic wars in (I think) every nation's battalion was Grenadiers, who were still the most veteran soldiers of the unit (size mattered less now that grenades were not being thrown, but the requirements were still there in part).

The Napoleoninc wars had no grenades being thrown institutionally, and they did not appear throughout the 19th century as firearms became orders of magnitude better. This really changed in the Russo-Japanese war, where grenades made their debut once again. Infantry tactics had moved away from mass blocks, and artillery no longer was at the fore to rake with canister (it was in the back, being more effective with fancy shells, but that is not important to this discussion). Infantry were dug into fortified positions or moving between pieces of cover, and grenades had become MUCH lighter as much better explosives than gunpowder became readily available to national armies. Russians and Japanese threw grenades at each other in increasing numbers through the war, and set a precedent for World War 1.

World War 1 made grenades a mandatory part of infantry doctrine, and while for a time individual soldiers were designated as specialist grenadiers, the military minds realized that grenades were so useful in modern warfare that just about every infantryman should carry them. There are still specialized grenadiers, using more esoteric explosives or carrying a grenade launcher, but just about every developed nation gives just about every infantryman grenades nowadays.