Battle of Cannae
On the other flank the Numidians engaged in a way that merely kept the Roman allied cavalry occupied. Hasdrubal kept his victorious Hispanic and Gallic cavalry under control and did not chase the retreating Roman right wing. Instead, he led them to the other side of the field to attack the socii cavalry still fighting the Numidians. Assailed from both sides, the allied cavalry broke before Hasdrubal could charge into contact and the Numidians pursued them off the field.
While the Carthaginian cavalry were in the process of defeating the Roman horsemen, the masses of infantry on both sides advanced towards each other in the center of the field. The wind from the east blew dust in the Romans' faces and obscured their vision. While the wind was not a major factor, the dust that both armies created would have been potentially debilitating to sight. Although it made seeing difficult, troops would still have been able to see others in the vicinity.
The dust was not the only psychological factor involved in battle. Because of the somewhat distant battle location, both sides were forced to fight on little sleep. Another Roman disadvantage was thirst caused by Hannibal's attack on the Roman encampment during the previous day. Furthermore, the massive number of troops would have led to an overwhelming amount of background noise. All of these psychological factors made battle especially difficult for the infantrymen.
The light infantry on both sides engaged in indecisive skirmishing, inflicting few casualties and quickly withdrawing through the ranks of their heavy infantry. As the Roman heavy infantry attacked, Hannibal stood with his men in the weak center and held them together in a controlled retreat. The crescent of Hispanic and Gallic troops buckled inwards as they gradually withdrew step by step. Knowing the superiority of the Roman infantry, Hannibal had instructed his infantry to withdraw deliberately, creating an even tighter semicircle around the attacking Roman forces. By doing so, he had turned the strength of the Roman infantry into a weakness. While the front ranks were gradually advancing, the bulk of the Roman troops began to lose their cohesion, as troops from the reserve lines advanced into the growing gaps. 
Soon they were compacted together so closely that they had little space to wield their weapons. In pressing so far forward in their desire to destroy the retreating and seemingly collapsing line of Hispanic and Gallic troops, the Romans had ignored (possibly due to the dust) the African troops that stood uncommitted on the projecting ends of this now-reversed crescent. 
This also gave the Carthaginian cavalry time to drive the Roman cavalry off on both flanks and attack the Roman center in the rear. The Roman infantry, now stripped of protection on both its flanks, formed a wedge that drove deeper and deeper into the Carthaginian semicircle, driving itself into an alley formed by the African infantry on the wings. At this decisive point, Hannibal ordered his African infantry to turn inwards and advance against the Roman flanks, creating an encirclement in one of the earliest known examples of a pincer movement.
When the Carthaginian cavalry attacked the Romans in the rear and the African flanking echelons assailed them on their right and left, the advance of the Roman infantry was brought to an abrupt halt. The Romans were henceforth enclosed in a pocket with no means of escape. The Carthaginians created a wall and began to systematically massacre them. Polybius wrote: "as their outer ranks were continually cut down, and the survivors forced to pull back and huddle together, they were finally all killed where they stood."
As Livy described, "So many thousands of Romans were dying... Some, whom their wounds, pinched by the morning cold, had roused, as they were rising up, covered with blood, from the midst of the heaps of slain, were overpowered by the enemy. Some were found with their heads plunged into the earth, which they had excavated; having thus, as it appeared, made pits for themselves, and having suffocated themselves." Victor Davis Hanson claims that nearly six hundred legionaries were slaughtered each minute until darkness brought an end to the bloodletting. Only 14,000 Roman troops managed to escape, including Scipio Africanus, who managed to escape the encirclement with 500 men, most of whom had cut their way through to the nearby town of Canusium.

Casualties: 

Roman: Polybius writes that of the Roman and allied infantry, 70,000 were killed, 10,000 captured, and "perhaps" 3,000 survived. He also reports that of the 6,000 Roman and allied cavalry, only 370 survived.
Livy wrote, "Forty-five thousand and five hundred foot, two thousand seven hundred horse, there being an equal number of citizens and allies, are said to have been slain." He also reports that 3,000 Roman and allied infantry and 1,500 Roman and allied cavalry were taken prisoner by the Carthaginians. Another 2,000 Roman fugitives were rounded up at the unfortified village of Cannae by Carthaginian cavalry commanded by Carthalo, 7,000 fell prisoner in the smaller Roman camp and 5,800 in the larger. Although Livy does not cite his source by name, it is likely to have been Quintus Fabius Pictor, a Roman historian who fought in and wrote about the Second Punic War. It is Pictor whom Livy names when reporting the casualties at the Battle of Trebia. 
In addition to the consul Paullus, Livy recorded that among the dead were 2 quaestors, 29 of the 48 military tribunes, some of consular rank, including the consul of the previous year, Gnaeus Servilius Geminus, and the former Magister equitum, Marcus Minucius Rufus, and 80 "senators or men who had held offices which would have given them the right to be elected to the Senate".
Later Roman and Greco-Roman historians largely follow Livy's figures. Appian gave 50,000 killed and "a great many" taken prisoner. Plutarch agreed, "50,000 Romans fell in that battle... 4,000 were taken alive in the field and 10,000 in the camps of both consuls". Quintilian: "60,000 men were slain by Hannibal at Cannae". Eutropius: "20 officers of consular and praetorian rank, 30 senators, and 300 others of noble descent, were taken or slain, as well as 40,000-foot-soldiers, and 3,500 horse".
Some modern historians, while rejecting Polybius's figure as flawed, are willing to accept Livy's figure. Other historians have come up with far lower estimates. In 1891, Cantalupi proposed Roman losses of 10,500 to 16,000. Samuels in 1990 also regarded Livy's figure as far too high, on the grounds that the cavalry would have been inadequate to prevent the Roman infantry escaping to the rear. He doubts that Hannibal even wanted a high death toll, as much of the army consisted of Italians whom Hannibal hoped to win as allies. Micheal Clodfelter also doubts the casualties of the Romans, citing the scarcity and unreliability of ancient sources, with him expressing that "are we really supposed to believe that Hannibal’s 50,000 Carthaginians slaughtered 48,000–70,000 Romans on a single afternoon on the field of Cannae, even if the battle did degenerate into a massacre in its final stages?".

Carthaginian: Livy recorded Hannibal's losses at "about 8,000 of his bravest men." Polybius reports 5,700 dead: 4,000 Gauls, 1,500 Hispanics and Africans, and 200 cavalry.

Aftermath: Never when the city was in safety was there so great a panic and confusion within the walls of Rome. I shall therefore shrink from the task, and not attempt to relate what in describing I must make less than the reality. The consul and his army having been lost at the Trasimenus the year before, it was not one wound upon another which was announced, but a multiplied disaster, the loss of two consular armies, together with the two consuls: and that now there was neither any Roman camp, nor general nor soldiery: that Apulia and Samnium, and now almost the whole of Italy, were in the possession of Hannibal. No other nation surely would not have been overwhelmed by such an accumulation of misfortune.
For a brief period, the Romans were in complete disarray. Their best armies in the peninsula had been destroyed, the few remnants severely demoralized, and the only remaining consul (Varro) completely discredited. As the story goes, Rome declared a national day of mourning as there was not a single person who was not either related to or acquainted with a person who had died. The Romans became so desperate that they resorted to human sacrifice, twice burying people alive at the Forum of Rome and abandoning an oversized baby in the Adriatic Sea (perhaps one of the last instances of human sacrifices by the Romans, apart from public executions of defeated enemies dedicated to Mars).

Within just three campaign seasons (20 months), Rome had lost one-fifth (150,000) of the entire population of male citizens over 17 years of age.