First held in 580 BCE, these games were in honour of Poseidon and were held near Argos. They were one of the great crown games, and their central location made them especially popular and crowded. There was an on-going feud between the Isthmian Games and the Olympics and athletes from Elis did not compete in the Isthmian Games. This feud was traced back to mythical times:
Heracles accomplished no brilliant feat in the war with Augeas. For the sons of Actor were in the prime of courageous manhood, and always defeated the allies under Heracles, until the Corinthians proclaimed the Isthmian truce, and the sons of Actor came as envoys to the meeting. Heracles set an ambush for then, at Cleonae and murdered them. As the murderer was unknown, Moline, more than any of the other children, devoted herself to detecting him.
When she discovered him, the Eleians demanded satisfaction for the crime from the people of Argos, for at the time Heracles had his home at Tiryns. When the Argives refused them satisfaction, the Eleians as an alternative pressed the Corinthians to exclude the people of Argos from the Isthmian Games. When they failed in this also, Moline is said to have laid curses on her countrymen, should they refuse to boycott the Isthmian Games. The curses of Molione are respected right down to the present day, and no athlete of Elis competes in the Isthmian Games.
Pausanias, Description of Greece 5.2.1-2
The popularity of the Isthmian Games and its very convenient location led to Nero using it to announce the freedom of Greece when he doing his tour of the games. (Freedom in this case meant local self-government and freedom from taxation, rather than freedom entirely from Roman rule. Although it was rescinded under the Flavians, it made Nero incredibly popular in Greece.)
In competition he observed the rules most scrupulously, never daring to clear his throat and even wiping the sweat from his brow with his arm. Once, indeed, during the performance of a tragedy, when he had dropped his sceptre but quickly recovered it, he was terribly afraid that he might be excluded from the competition because of his slip, and his confidence was restored only when his accompanist swore that it had passed unnoticed amid the delight and applause of the people. When he won he made the announcement himself; and for that reason he always took part in the contests of the heralds. To obliterate the memory of all other victors in the games and leave no trace of them, their statues and busts were all thrown down by his order, dragged off with hooks, and cast into toilets. He also drove a chariot in many places, and a ten-horse chariot team at Olympia, although in one of his own poems he had criticized Mithridates for just that thing. But after he had been thrown from the car and put back in it, he was unable to hold out and gave up before the end of the course; but he received the crown just the same. On his departure he presented the entire province with freedom and at the same time gave the judges Roman citizenship and a large sum of money. These favours he announced in person on the day of the Isthmian Games, standing in the middle of the stadium.
Suetonius, Life of Nero 24
Short summary of the games