Battle of Cannae
After various political experiments, Scipio Africanus was made general-in-chief of the Roman armies in Africa, and was assured this role for the duration of the war. This appointment may have violated the constitutional laws of the Roman Republic but, as Delbrück wrote, it "effected an internal transformation that increased her military potentiality enormously" while foreshadowing the decline of the Republic's political institutions. Furthermore, the battle exposed the limits of a citizen-militia army. Following Cannae, the Roman army gradually developed into a professional force.

Status in military history: Cannae is as famous for Hannibal's tactics as it is for the role it played in Roman history. Not only did Hannibal inflict a defeat on the Roman Republic in a manner unrepeated for over a century until the lesser-known Battle of Arausio, but the battle also has acquired a significant reputation in military history. As military historian Theodore Ayrault Dodge wrote:

Few battles of ancient times are more marked by ability... than the battle of Cannae. The position was such as to place every advantage on Hannibal's side. The manner in which the far from perfect Hispanic and Gallic foot was advanced in a wedge in echelon... was first held there and then withdrawn step by step, until it had reached the converse position... is a simple masterpiece of battle tactics. The advance at the proper moment of the African infantry, and its wheel right and left upon the flanks of the disordered and crowded Roman legionaries, is far beyond praise. The whole battle, from the Carthaginian standpoint, is a consummate piece of art, having no superior, few equal, examples in the history of war.
Will Durant wrote, "It was a supreme example of generalship, never bettered in history... and it set the lines of military tactics for 2,000 years".
Hannibal's double envelopment at Cannae is often viewed as one of the greatest battlefield maneuvers in history, and is cited as the first successful use of the pincer movement within the Western world to be recorded in detail.

"Cannae model": Apart from being one of the greatest defeats inflicted on Roman arms, Cannae represents the archetypal battle of annihilation, a strategy that has rarely succeeded since. As Dwight D. Eisenhower, the Supreme Commander of the Allied Expeditionary Force in World War II, wrote, "Every ground commander seeks the battle of annihilation; so far as conditions permit, he tries to duplicate in modern war the classic example of Cannae". "Cannae" has become a byword for military success, and the battle is studied in military academies around the world. The notion that an entire army could be encircled and annihilated within a single stroke led to a fascination among Western generals for centuries, including Frederick the Great and Helmuth von Moltke, who attempted to create their own "Cannae".
Delbrück's seminal study of the battle influenced German military theorists, particularly the Chief of the German General Staff, Alfred von Schlieffen, whose "Schlieffen Plan" was inspired by Hannibal's double envelopment maneuver. Schlieffen believed that the "Cannae model" would continue to be applicable in maneuver warfare throughout the 20th century:

A battle of annihilation can be carried out today according to the same plan devised by Hannibal in long forgotten times. The enemy front is not the goal of the principal attack. The mass of the troops and the reserves should not be concentrated against the enemy front; the essential is that the flanks be crushed. The wings should not be sought at the advanced points of the front but rather along the entire depth and extension of the enemy formation. The annihilation is completed through an attack against the enemy's rear... To bring about a decisive and annihilating victory requires an attack against the front and against one or both flanks...
Schlieffen later developed his own operational doctrine in a series of articles, many of which were translated and published in a work entitled Cannae.
In 1991, General Norman Schwarzkopf Jr., commander of coalition forces in the Gulf War, cited Hannibal's triumph at Cannae as inspiration for the rapid and successful coalition operations during the conflict.

Historical sources: There are three main accounts of the battle, none of them contemporary. The closest is Polybius, who wrote his account 50 years after the battle. Livy wrote in the time of Augustus, and Appian later still. Appian's account describes events that have no relation with those of Livy and Polybius. Polybius portrays the battle as the nadir of Roman fortunes, perhaps to emphasise the subsequent Roman recovery—some historians contend that his casualty figures are exaggerated—"more symbolic than factual". 
Livy portrays the Senate in heroic terms and assigns blame for the Roman defeat to the low-born Varro. This lifts blame from the Roman soldiers, whom Livy idealizes. Scholars tend to discount Appian's account. The verdict of Philip Sabin—"a worthless farrago"—is typical.
Although he has no connected narrative of the battle, Plutarch provides a number of details about Cannae in his Parallel Lives, specifically the essays "Fabius" and "Aemilius Paulus".
Historian Martin Samuels has questioned whether it was in fact Varro in command on the day on the grounds that Paullus may have been in command on the right. The warm reception that Varro received after the battle from the Senate was in striking contrast to the savage criticism meted out to other commanders. Samuels doubts whether Varro would have been received with such warmth had he been in command. Gregory Daly notes that, in the Roman military, the right was always the place of command. He suggests that at the Battle of Zama Hannibal claimed to have fought Paullus at Cannae and concludes that it is impossible to be sure who was in command on the day.

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External links: 
Cannae – a treatise by General Fieldmarshal Count Alfred von Schlieffen
Archaeological site believed to be where the battle took place
Battle At Cannae Mommsen History of Rome. Book 03 From the Union of Italy to the Subjugation of Carthage and the Greek States, p. 50