In 1726, the Frenchman, Cesar de Saussure, witnessed a hanging in London. Later, he recorded the details of the execution for posterity:
On the day of execution the condemned prisoners, wearing a sort of white linen shirt over their clothes and a cap on their heads, are tied two together and placed on carts with their backs to the horses’ tails. These carts are guarded and surrounded by constables and other police officers on horseback, each armed with a sort of pike. In this way part of the town is crossed, and Tyburn, which is a good half-mile from the last suburb, is reached, and here stands the gibbet…
The chaplain who accompanies the condemned men is also on the cart; he makes pray and sings a few verses of the Psalms. Relatives are permitted to mount the cart and take farewell. When the time is up – that is to about a quarter of an hour – the chaplain and relations get off the cart, the executioner covers the eyes and faces of the prisoners with their caps lashes the horses that draw the cart, which slips from under the condemned men’s feet, and in this way they remain all hanging together. You often see friends and relations tugging at the hanging men’s feet so that they should die quicker not suffer. 
In the 20th century, death by hanging was intended to be quick. The drop and jerk were designed to dislocate the first two vertebrae in the neck, severing the spinal cord at that point. Because the nerves which control breathing are located beneath the 3rd, 4th and 5th vertebrae, air can no longer move in and out of the lungs. Death occurs within minutes.
In the 18th century, those who died on the scaffold were not as lucky. The time it took to die depended on several factors—the knot, the rope, the drop and the jerk—none of which had been perfected during this period. Thus, those who were hanged typically suffered slow, agonizing deaths as they gradually choked—their necks unbroken and their lungs still gasping for air. As long as the muscles in the neck stayed strong, a person could dangle at the end of a rope for upwards of thirty minutes before he or she died.
Even at that, death was not always guaranteed. Although it was rare, there were certainly instances of people being cut down from the gallows, only to miraculously resuscitate on the dissecting table. (Read more here).
The hyoid bone (pictured below) is located inside the larynx, and sits at the base of the tongue. This delicate bone is the only one in the body which is not connected to another. Encased in muscles and ligaments, it is very well protected from breakage and injury. However, during strangulation or hanging, the hyoid snaps, resulting in ‘the hangman’s fracture’.
Hyoid bone, 18th century.
The last person to be hanged in the Western world was William Bailey, who had been found guilty of double homicide. On the day of execution, a 220 pound Bailey climbed 23 steps to the wooden platform above. There, with a noose around his neck and a black hood over his head, he followed hundreds of thousands who had preceded him in this untimely method of death.
He died 25 January 1996.
1. Cesar de Saussure, A Foreign View of England in the Reigns of George I and George II (1902), reprinted in: Charles-Edwards, T. and B. Richardson, They Saw it Happen, An Anthology of Eyewitness’s Accounts of Events in British History 1689-1897 (1958).