Each myth is presented in the voice of a narrator writing under the Antonines, such as Plutarch or Pausanias, with citations of the classical sources. Each myth is followed by an interpretation of its origin and significance, in the terms of Graves' other essays on mythology, such as The White Goddess.
Graves interpreted Bronze Age Greece as changing from a matriarchal society under the Pelasgians, to a matrilineal one, to a patriarchal one under continual pressure from victorious Greek-speaking tribes. In the second stage, local kings came to each settlement as foreign princes, reigned by marrying the hereditary queen, who represented the Triple Goddess, and were ritually slain by the next king after a limited period, originally six months. Kings managed to evade the sacrifice for longer and longer periods, often by sacrificing substitutes, and eventually converted the Queen, priestess of the Goddess, into a subservient and chaste wife, and in the final stage had legitimate sons to reign after them.
The Greek Myths presents the myths as stories from the ritual of all three stages, and often as historic records of the otherwise unattested struggles between the Greek Kings and the Moon-priestesses. In some cases, Graves conjectures a process of "iconotropy" or image-turning, by which a hypothetical cult image of the matriarchal or matrilineal period has been misread by later Greeks in their own terms. Thus, for example, he conjectures an image of divine twins struggling in the womb of the Horse-Goddess, which later gave rise to the Trojan Horse myth.
Graves' retellings have been widely praised: "The stories themselves have been presented in a lively and attractive manner, with an effect of candour and intimacy very like that of Samuel Butler's translations of Homer. Even some of the harshest critics of his scholarship agree: "the paraphrases themselves are wittily written, and take a twinkly delight in promoting extra-canonical alternative versions of familiar stories.
Ted Hughes and other poets have found the system of The White Goddess congenial; The Greek Myths contains about a quarter of that system, and does not include the method of composing poetry.
But The Greek Myths has been heavily criticised both during and after the lifetime of the author. These have primarily deprecated Graves' personal interpretations, which are, in the words of one of them, "either the greatest single contribution that has ever been made to the interpretation of Greek myth or else a farrago of cranky nonsense; I fear that it would be impossible to find any classical scholar who would agree with the former diagnosis." His etymologies are questionable, and his largely intuitive division between "true myth" and other sorts of story is viewed as arbitrary, taking myths out of the context in which we now find them. The basic assumption that explaining mythology requires any "general hypothesis", whether Graves' or some other, is also disputed.
H. J. Rose, and in this he is supported by several of the other critics cited, finds even the scholarship of the retellings questionable. Graves presents The Greek Myths as an updating of William Smith's Dictionary of Greek and Roman Biography and Mythology (originally published 1844) and calls it still "the standard work in English", never brought up to date; Rose finds this deprecable, and sees no sign that Graves has heard of the Oxford Classical Dictionary or any of the "various compendia of mythology, written in, or translated into our tongue since 1844." He finds many omissions and some clear errors, most seriously ascribing to Sophocles the argument to his Ajax (Graves §168.4); this evaluation has been repeated by other critics since.
Graves dismissed the reactions of classical scholars, arguing that by definition they lacked the poetic capacity to forensically examine mythology.