Of two works known under the title Peri Apiston (On Unbelievable Tales) that of Heraclitus Paradoxographus is the lesser-known. Palaephatus was the author of a better-known work of paradoxography with the same title, mentioned more often in antiquity.
Heraclitus' Peri Apiston treats Greek mythology in the rationalizing manner that appealed to Christian apologists, in simple language and thought. The text survives in a single 13th-century manuscript in the Vatican Library; it has minor imperfections, and it may well be a late Byzantine epitome of a longer work. Of the author nothing is known, although he appears to belong to the late 1st or 2nd century CE; he is unlikely to be any of the other men of the name of Heraclitus known from classical antiquity. The 12th-century Byzantine scholar and commentator on Homer, Eustathius of Thessalonica, is the only scholar who mentions him, as "the Heraclitus who proposes to render unbelievable tales believable."
The text includes thirty-nine items in which familiar myths are briefly told and then explained; Heraclitus has four methods of explanation, all prominent in late Hellenistic and Roman interpretations: rationalization (that the myth represents a misunderstanding of a natural event), euhemerism, allegory, or fanciful etymology. All these techniques of exegesis were later adopted and developed by Christian theologians of Late Antiquity. Among extant mythographical collections this text is of particular interest precisely because it exemplifies in brief compass such a range of ancient strategies for the interpretation of myth.