Antique Artillery Uses
From Antiquity to roughly the medieval era, artillery is primarily a siege weapon or used in defense of fortified positions. In siege they were used to propel items over the walls, while in defense they were used to mow down assaulting infantry trying to climb over the walls. During this time artillery is mostly a 'static' weapon, moved or constructed on-site, and needs to be protected by other units.
In antique-era games, Artillery provides a harassing effect during sieges, but by themselves artillery is easily dispatched. On the battlefield, Artillery will not be found.
Early Gunpowder Artillery
Sometime during the renaissance period, from roughly early 1400's on, artillery became powerful enough to bring down castle walls on their own. This changed the role of artillery from a siege 'nice to have', to a requirement. Artillery was heavy and hard to move, but could be found in almost all European armies.
A disadvantage of the gunpowder weapons is the inability to build them 'on-site'. Suddenly, the logistics of a siege became more complex as artillery units, and their ammunition, must be transported to the siege location. On the battlefield, artillery was still too heavy to move and too inaccurate. Given the size, unwieldiness, and cost of these weapons, a great tactic is to engage the weapon before it arrives at its destination. As such, armies formed around the artillery pieces as protection for them to arrive at their location.
Late Gunpowder Era Artillery
From roughly the 17th century to The Great War (WWI), advances in artillery permitted them to become lighter, more powerful, and more accurate. These, coupled with improved munition types, transformed artillery to a battlefield weapon. Whereas before artillery was to be protected, now it could effectively fight on the battlefield.
Still, artillery never "held the line" without support. Instead, artillery became a strong and powerful balancing factor. Able to engage the enemy at long range, artillery demoralized the enemy. At close range a few canon loaded with canister rounds could devastate an infantry or cavalry charge. Once in place during a battle, artillery could be moved short distances effectively, but long advances or retreats were impossible. This made Artillery a 'set-piece' unit on the battlefield.
The weakness of artillery at this stage is the low rate of fire and set up time. Although some units could achieve fairly good rates of fire over short periods of time, it could not be maintained indefinitely. Additionally, the setup time required to prepare artillery for firing meant the opposing forces could 'take cover' to reduce their exposure to fire. As an example, during the American Civil War, only about 10% of battlefield casualties were caused by artillery.
Sea Artillery
Artillery was quickly adopted by naval units. Prior to canons at sea, the primary method of taking a ship was to board it or ram it. Ramming was as dangerous to the attacker as the defender. Boarding usually meant the unit with the larger crew would win.
The introduction of canons permitted ships to attack from further away than the boarding and ram ships. It also allowed ships to bombard forts and buildings on shore, purportedly in support of ground troops assaulting at the same time.
Modern Artillery
In the modern age, from WWI onwards, artillery came into its own. Mobile artillery, what would have been an artillery canon on wheels, became the tank and self-propelled gun we know today. Artillery hurls shells miles.
Rocket Artillery
Rockets were first used around the mid-1200s by the Chinese. However, they were probably more an instrument of fear than a true damaging force, much like elephants were to Alexander the Great. In World War II, with the German Nebelwerfer and Soviet Katyusha systems, rockets added the a capability of doing physical damage to their fear aspect. The fear of rockets lies not only in their destructive capacity, but the fact a volley of rockets lands without warning and in a relatively small area. Modern rockets are capable of traveling hundreds of miles, or around the world if the ICBM is considered a form of rocket artillery. Modern conventional rockets can deliver a variety of payloads and, unlike their predecessors, can deliver it with precision accuracy.
Aircraft
Aircraft were the earliest "super long range" form of artillery. During WWII, bombers could travel hundreds of miles from Britain to Germany, dropping thousands of pounds of explosives on the way. In the wars of Korea and Vietnam, radio communications allowed aircraft to coordinate with front line infantry, filling the role of artillery by bringing heavy explosives to a points on the front lines. In this regard, aircraft may be viewed as a form of artillery.