He was the son of Ascondus, and was the heir to a large fortune, which he is said to have renounced to live a life of Cynic poverty in Athens.

Diogenes Laërtius[6] preserves several different accounts of this story; one of them has Crates giving his money away to the citizens of Thebes, apparently after seeing the beggar king Telephus in a tragedy; whereas another account has him placing his money in the hands of a banker, with the agreement that he should deliver it to his sons, unless they too became philosophers, in which case he should distribute it among the poor.

We learn that Crates is supposed to have initiated his son into sex by taking him to a brothel,[16] and he allowed his daughter a month's trial marriage to potential suitors.

[26] Crates was also the author of some philosophical tragedies, and some smaller poems apparently called Games (Ancient Greek: Παίγνια, romanized: Paignia).

He taught a simple asceticism, which seems to have been milder than that of his predecessor Diogenes: And therefore Crates replied to the man who asked, "What will be in it for me after I become a philosopher?"

[28] This jest would later be the cause of much satire, as in book 4 of Athenaeus' Deipnosophistae where a group of Cynics sit down for a meal and are served course after course of lentil soup.

But whereas Solon wished for prosperity, reputation, and "justly acquired possessions", Crates had typically Cynic desires: Glorious children of Memory and Olympian Zeus, Muses of Pieria, listen to my prayer!

[30]There are also several fragments surviving of a poem Crates wrote describing the ideal Cynic state which begins by parodying Homer's description of Crete.

[31] Crates' city is called Pera, which in Greek refers to the beggar's wallet which every Cynic carried: There is a city Pera in the midst of wine-dark Tuphos, Fair and fruitful, filthy all about, possessing nothing, Into which no foolish parasite ever sails, Nor any playboy who delights in a whore's ass, But it produces thyme, garlic, figs, and bread, For which the citizens do not war with each other, Nor do they possess arms, to get cash or fame.

A fictional biography of Crates was written by French author Marcel Schwob in his 1896 work Vies imaginaires.