Military history
A rule of thumb is that if your enemy has a potentially war winning weapon, you have to either match it or neutralize it.

Ancient era: Chariots originated around 2000 BC. The chariot was an effective, fast weapon; while one man controlled the maneuvering of the chariot, a second bowman could shoot arrows at enemy soldiers. These became crucial to the maintenance of several governments, including the New Egyptian Kingdom and the Shang dynasty and the nation states of the early to middle Zhou dynasty.
Some of the military unit types and technologies which were developed in the ancient world are:

Slinger
Hoplite
Auxiliaries
Infantry
Archery
Chariots
Cavalry
For settled agrarian civilizations, the infantry became the core of military action. The infantry started as opposing armed groups of soldiers underneath commanders. The Greeks and early Romans used rigid, heavily armed phalanxes. The Macedonians and Hellenistic states would adopt phalanx formations with sarissa pikemen. The Romans would later adopt more flexible maniples from their neighbors which made them extremely successful in the field of battle. The kingdoms of the Warring States in East Asia also adopted infantry combat, a transition from chariot warfare from centuries earlier.
Archers were a major component of many ancient armies, notably those of the Persians, Scythians, Egyptians, Nubians, Indians, Chinese, Koreans and Japanese.
Cavalry became an important tool. In the Sicilian Expedition, led by Athens in an attempt to subdue Syracuse, the well-trained Syracusan cavalry became crucial to the success of the Syracusans. Macedonian Alexander the Great effectively deployed his cavalry forces to secure victories. In battles such as the Battle of Cannae of the Second Punic War, and the Battle of Carrhae of the Roman-Persian Wars, the importance of the cavalry would be repeated.
There were also horse archers, who had the ability to shoot on horseback—the Parthians, Scythians, Mongols, and other various steppe people were especially fearsome with this tactic. By the 3rd–4th century AD, heavily armored cavalry became widely adopted by the Parthians, Sasanians, Byzantines, Eastern Han dynasty and Three Kingdoms, etc.
The early Indo-Iranians developed the use of chariots in warfare. The scythed chariot was later invented in India and soon adopted by the Persians.
War elephants were sometimes deployed for fighting in ancient warfare. They were first used in India and later adopted by the Persians. War elephants were also used in the Battle of the Hydaspes River, and by Hannibal in the Second Punic War against the Romans. One of the most important military transactions of the ancient world was Chandragupta Maurya's gift of 500 elephants to Seleucus I Nicator.

Naval warfare was often crucial to military success. Early navies used sailing ships without cannons; often the goal was to ram the enemy ships and cause them to sink. There was human oar power, often using slaves, built up to ramming speed. Galleys were used in the 3rd millennium BC by the Cretans. The Greeks later advanced these ships.
In 1210 BC, the first recorded naval battle was fought between Suppiluliuma II, king of the Hittites, and Cyprus, which was defeated. In the Greco-Persian Wars, the navy became of increasing importance.
Triremes were involved in more complicated sea-land operations. Themistocles helped to build up a stronger Greek navy, composed of 310 ships, and defeated the Persians at the Battle of Salamis, ending the Persian invasion of Greece.
In the First Punic War, the war between Carthage and Rome started with an advantage to Carthage because of their naval experience. A Roman fleet was built in 261 BC, with the addition of the corvus that allowed Roman soldiers to board enemy ships. The bridge would prove effective at the Battle of Mylae, resulting in a Roman victory.
The Vikings, in the 8th century AD, invented a ship propelled by oars with a dragon decorating the prow, hence called the Drakkar. The 12th century AD Song dynasty invented ships with watertight bulkhead compartments while the 2nd century BC Han dynasty invented rudders and sculled oars for their warships.
Fortifications are important in warfare. Early hill-forts were used to protect inhabitants in the Iron Age. They were primitive forts surrounded by ditches filled with water. Forts were then built out of mud bricks, stones, wood, and other available materials. Romans used rectangular fortresses built out of wood and stone. As long as there have been fortifications, there have been contraptions to break in, dating back to the times of Romans and earlier. Siege warfare is often necessary to capture forts.

Middle-ages: Some of the military unit types and technologies which were used in the medieval period are:

Artillery
Cataphract
Condottieri
Fyrd
Rashidun
Mobile guard
Mamluk
Janissary
Knight (see also: Chivalry)
Crossbow
Pikeman
Samurai
Sipahi
Trebuchet
Bows and arrows were often used by combatants. Egyptians shot arrows from chariots effectively. The crossbow was developed around 500 BC in China, and was used heavily in the Middle Ages. The English/Welsh longbow from the 12th century also became important in the Middle Ages. It helped to give the English a large early advantage in the Hundred Years' War, even though the English were eventually defeated. The Battle of Crécy and the Battle of Agincourt are excellent examples of how to destroy an enemy using a longbow. It dominated battlefields for over a century.

Gunpowder: There is evidence for gunpowder evolving slowly from formulations by Chinese alchemists as early as the 4th century, at first as experiments for life force and metal transmutation, and later experiments as pyrotechnics and incendiaries. By the 10th century, the developments in gunpowder led to many new weapons that were improved over time. The Chinese used incendiary devices based on this in siege warfare against the Mongols starting in the mid 13th century. "Pots with wicks of flax or cotton were used, containing a combination of sulfur, saltpeter (potassium nitrate), aconitine, oil, resin, ground charcoal and wax." Joseph Needham argued the Chinese were able to destroy buildings and walls using such devices. Such experimentation was not present in Western Europe, where the combination of saltpeter, sulfur and charcoal were used exclusively for explosives and as a propellant in firearms. What the Chinese often referred to as the "fire drug" arrived in Europe, fully fleshed out, as gunpowder.
Cannons were first used in Europe in the early 14th century, and played a vital role in the Hundred Years' War. The first cannons were simply welded metal bars in the form of a cylinder, and the first cannonballs were made of stone. By 1346, at the Battle of Crécy, the cannon had been used; at the Battle of Agincourt they would be used again.
The first infantry firearms, from fire lances to hand cannons, were held in one hand, while the explosive charge was ignited by a lit match or hot coal held in the other hand. In the mid-15th century came the matchlock, allowing the gun to be aimed and fired while held steady with both hands, as used in the arquebus. Starting about 1500, clever but complicated firing mechanisms were invented to generate sparks to ignite the powder instead of a lit match, starting with the wheel lock, snaplock, snaphance, and finally the flintlock mechanism, which was simple and reliable, becoming standard with the musket by the early 17th century.
At the beginning of the 16th century, the first European fire ships were used. Ships were filled with flammable materials, set on fire, and sent to enemy lines. This tactic was successfully used by Francis Drake to scatter the Spanish Armada at the Battle of Gravelines, and would later be used by the Chinese, Russians, Greeks, and several other countries in naval battles.
Naval mines were invented in the 17th century, though they were not used in great numbers until the American Civil War. They were used heavily in the First and Second World Wars. Air-deployed naval mines were used to mine the North Vietnamese port of Haiphong during the Vietnam War. The Iraqi Navy of Saddam Hussein used naval mines extensively during the Tanker War, as part of the Iran–Iraq War.
The first navigable submarine was built in 1624 by Cornelius Drebbel, it could cruise at a depth of 15 feet (5 m). However, the first military submarine was constructed in 1885 by Isaac Peral.
The Turtle was developed by David Bushnell during the American Revolution. Robert Fulton then improved the submarine design by creating the Nautilus.
The Howitzer, a type of field artillery, was developed in the 17th century to fire high trajectory explosive shells at targets that could not be reached by flat trajectory projectiles.