When you Google most "greatest" topics in ancient history, you need to insert the keyword "ancient". Not so for warriors or military leaders, although the medieval, rather than ancient, Genghis Khan may dominate your list. Great ancient military leaders and tacticians have had a lasting impact on the military; modern military schools study some of their battle tactics.
The following are the men I consider the greatest warriors, military leaders, or tacticians in the (ancient) world.
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Great warriors make the best conquerors. For fun, take this Which Ancient Conqueror Are You quiz.

Clipart.comSacked Rome
Alaric, the Visigoth king, knew it was foretold that he would conquer Rome, but despite his destiny, Alaric tried to negotiate peacefully with the rulers of Rome.

Public Domain. Courtesy of Wikipedia.Conquered Most of the Known World
Alexander the Great, King of Macedon from 336 - 323 B.C., may claim the title of the greatest military leader the world has ever known. His empire spread from Gibraltar to the Punjab, and he made Greek the lingua franca of his world.

Public Domain. Courtesy of Wikipedia.Scourge of God
Attila was the fierce 5th century leader of the barbarian group known as the Huns who struck fear in the hearts of the Romans as he plundered everything in his path, invaded the Eastern Empire and then crossed the Rhine into Gaul.

Clipart.comFounder of the Persian Empire
Cyrus conquered the Median Empire and Lydia, becoming Persian king by 546 B.C. Seven years later, Cyrus defeated the Babylonians and liberated the Jews.

Clipart.comAlmost Conquered Rome
Hannibal was the leader of the Carthaginian forces against Rome in the Second Punic War. Hannibal almost overpowered Rome and was considered Rome's greatest enemy.

Clipart.comConquered Gaul
Julius Caesar not only led the army and won many battles, but he wrote about his military adventures. It's from his description of the wars of the Romans against the Gauls (in modern France) that we get the familiar line "Gallia est omnis divisa in partes tres" 'all Gaul is divided into 3 parts,' which Caesar proceeded to conquer.

Public Domain. Courtesy of WikipediaReformed the Roman Army
Marius needed more troops, so he instituted policies that changed the complexion of the Roman army. Instead of requiring a minimum property qualification of his soldiers, Marius recruited poor soldiers with promises of pay and land. To serve as military leader against Rome's enemies, Marius was elected consul a record-breaking 7 times.
Clipart.comBeat Hannibal
Scipio Africanus is the Roman commander who defeated Hannibal at the Battle of Zama in the Second Punic War via tactics he'd learned from the enemy. Since Scipio's victory was in Africa, following his triumph he was allowed to take the agnomen Africanus. He later received the name Asiaticus when serving under his brother Lucius Cornelius Scipio against Antiochus III of Syria in the Seleucid War.
Public Domain. Courtesy of Wikipedia [en.wikipedia.org/wiki/Image:Suntzu2.jpg].Wrote the Art of War
Sun Tzu wrote about Chinese military strategy and martial arts in
The Art of War, in the 5th century B.C., in ancient China. The book has been influential ever since. Sun Tzu was a general and is reported to have taught strict military discipline to women.

Clipart.comExpanded the Roman Empire
Trajan, emperor and soldier, spent most of his life involved in campaigns. Trajan's major campaigns as emperor were against the Dacians, in 106, which vastly increased the Roman imperial coffers, and against the Parthians, beginning in 113. Under Trajan the Roman Empire reached its greatest extent.