Siege
Ancient period: 

The necessity of city walls: The Assyrians deployed large labour forces to build new palaces, temples, and defensive walls. Some settlements in the Indus Valley civilization were also fortified. By about 3500 BC, hundreds of small farming villages dotted the Indus River floodplain. Many of these settlements had fortifications and planned streets.
The stone and mud brick houses of Kot Diji were clustered behind massive stone flood dikes and defensive walls, for neighbouring communities quarrelled constantly about the control of prime agricultural land. Mundigak (c. 2500 BC) in present-day south-east Afghanistan has defensive walls and square bastions of sun-dried bricks.
City walls and fortifications were essential for the defence of the first cities in the ancient Near East. The walls were built of mudbricks, stone, wood, or a combination of these materials, depending on local availability. They may also have served the dual purpose of showing potential enemies the might of the kingdom. The great walls surrounding the Sumerian city of Uruk gained a widespread reputation. The walls were 9.5 km (5.9 mi) in length, and up to 12 m (39 ft) in height.
Later, the walls of Babylon, reinforced by towers, moats, and ditches, gained a similar reputation. In Anatolia, the Hittites built massive stone walls around their cities atop hillsides, taking advantage of the terrain. In Shang dynasty China, at the site of Ao, large walls were erected in the 15th century BC that had dimensions of 20 m (66 ft) in width at the base and enclosed an area of some 1,900 m (2,100 yd) squared. The ancient Chinese capital for the State of Zhao, Handan, founded in 386 BC, also had walls that were 20 m (66 ft) wide at the base; they were 15 m (49 ft) tall, with two separate sides of its rectangular enclosure at a length of 1,400 m (1,530 yd).
The cities of the Indus Valley Civilization showed less effort in constructing defences, as did the Minoan civilization on Crete. These civilizations probably relied more on the defence of their outer borders or sea shores. Unlike the ancient Minoan civilization, the Mycenaean Greeks emphasized the need for fortifications alongside natural defences of mountainous terrain, such as the massive Cyclopean walls built at Mycenae and other adjacent Late Bronze Age (c. 1600–1100 BC) centers of central and southern Greece.

Archaeological evidence: Although there are depictions of sieges from the ancient Near East in historical sources and in art, there are very few examples of siege systems that have been found archaeologically. Of the few examples, several are noteworthy:

The late 9th-century BC siege system surrounding Tell es-Safi/Gath, Israel, consists of a 2.5 km (1.6 mi) long siege trench, towers, and other elements, and is the earliest evidence of a circumvallation system known in the world. It was apparently built by Hazael of Aram Damascus, as part of his siege and conquest of Philistine Gath in the late 9th century BC (mentioned in II Kings 12:18).
The late 8th-century BC siege system surrounding the site of Lachish (Tell el-Duweir) in Israel, built by Sennacherib of Assyria in 701 BC, is not only evident in the archaeological remains, but is described in Assyrian and biblical sources and in the reliefs of Sennacherib's palace in Nineveh.
The Siege of Alt-Paphos, Cyprus by the Persian army in the 4th century BC.

Depictions: The earliest representations of siege warfare have been dated to the Protodynastic Period of Egypt, c. 3000 BC. These show the symbolic destruction of city walls by divine animals using hoes.
The first siege equipment is known from Egyptian tomb reliefs of the 24th century BC, showing Egyptian soldiers storming Canaanite town walls on wheeled siege ladders. Later Egyptian temple reliefs of the 13th century BC portray the violent Siege of Dapur, a Syrian city, with soldiers climbing scale ladders supported by archers.
Assyrian palace reliefs of the 9th to 7th centuries BC display sieges of several Near Eastern cities. Though a simple battering ram had come into use in the previous millennium, the Assyrians improved siege warfare and used huge wooden tower-shaped battering rams with archers positioned on top.
In ancient China, sieges of city walls (along with naval battles) were portrayed on bronze 'hu' vessels, like those found in Chengdu, Sichuan in 1965, which have been dated to the Warring States period (5th to 3rd centuries BC).

Tactics: 

Offensive: An attacker's first act in a siege might be a surprise attack, attempting to overwhelm the defenders before they were ready or were even aware there was a threat. This was how William de Forz captured Fotheringhay Castle in 1221.
The most common practice of siege warfare was to lay siege and just wait for the surrender of the enemies inside or, quite commonly, to coerce someone inside to betray the fortification. During the medieval period, negotiations would frequently take place during the early part of the siege. An attacker – aware of a prolonged siege's great cost in time, money, and lives – might offer generous terms to a defender who surrendered quickly. The defending troops would be allowed to march away unharmed, often retaining their weapons. However, a garrison commander who was thought to have surrendered too quickly might face execution by his own side for treason.
As a siege progressed, the surrounding army would build earthworks (a line of circumvallation) to completely encircle their target, preventing food, water, and other supplies from reaching the besieged city. If sufficiently desperate as the siege progressed, defenders and civilians might have been reduced to eating anything vaguely edible – horses, family pets, the leather from shoes, and even each other.
The Hittite siege of a rebellious Anatolian vassal in the 14th century BC ended when the queen mother came out of the city and begged for mercy on behalf of her people. The Hittite campaign against the kingdom of Mitanni in the 14th century BC bypassed the fortified city of Carchemish. If the main objective of a campaign was not the conquest of a particular city, it could simply be passed by. When the main objective of the campaign had been fulfilled, the Hittite army returned to Carchemish and the city fell after an eight-day siege.
Disease was another effective siege weapon, although the attackers were often as vulnerable as the defenders. In some instances, catapults or similar weapons were used to fling diseased animals over city walls in an early example of biological warfare. If all else failed, a besieger could claim the booty of his conquest undamaged, and retain his men and equipment intact, for the price of a well-placed bribe to a disgruntled gatekeeper. The Assyrian siege of Jerusalem in the 8th century BC came to an end when the Israelites bought them off with gifts and tribute, according to the Assyrian account, or when the Assyrian camp was struck by mass death, according to the Biblical account. Due to logistics, long-lasting sieges involving a minor force could seldom be maintained. A besieging army, encamped in possibly squalid field conditions and dependent on the countryside and its own supply lines for food, could very well be threatened with the disease and starvation intended for the besieged.

To end a siege more rapidly, various methods were developed in ancient and medieval times to counter fortifications, and a large variety of siege engines was developed for use by besieging armies. Ladders could be used to escalade over the defenses. Battering rams and siege hooks could also be used to force through gates or walls, while catapults, ballistae, trebuchets, mangonels, and onagers could be used to launch projectiles to break down a city's fortifications and kill its defenders. A siege tower, a substantial structure built to equal or greater height than the fortification's walls, could allow the attackers to fire down upon the defenders and also advance troops to the wall with less danger than using ladders.
In addition to launching projectiles at the fortifications or defenders, it was also quite common to attempt to undermine the fortifications, causing them to collapse. This could be accomplished by digging a tunnel beneath the foundations of the walls, and then deliberately collapsing or exploding the tunnel. This process is known as mining. The defenders could dig counter-tunnels to cut into the attackers' works and collapse them prematurely.
Fire was often used as a weapon when dealing with wooden fortifications. The Roman Empire used Greek fire, which contained additives that made it hard to extinguish. Combined with a primitive flamethrower, it proved an effective offensive and defensive weapon. A sallying out might also occur with such weapons, or if the siege was of a location on a coastline, from ships launched from the harbor of the location.

Defensive: The universal method for defending against siege is the use of fortifications, principally walls and ditches, to supplement natural features. A sufficient supply of food and water was also important to defeat the simplest method of siege warfare: starvation.