National Geographic piece about Delphi

Pythia - The Delphic Oracle with laurel leaf

Nat Geo has a fine story this month about Delphi, the navel of the Earth -- worth a look given that The Eumenides, when we get to it, opens with a long speech of the Pythia, followed by the appearance of Apollo. The article echoes the opening of that play, though it has a variant on the genealogy of the presiding deities of the site:

. . . this impressive spot in central Greece (about 100 miles northwest of Athens) was originally sacred to Gaea, mother goddess of the earth, who placed her son Python, a serpent, as a guard for Delphi and its oracle. Apollo, god of light and music, slew the serpent and took over the site for himself. Priestesses who served Apollo there were called the “Pythia,” named in honor of Gaea’s vanquished son. Throughout the classical world spread the belief that these priestesses channeled prophecies from Apollo himself. (Read about the science behind the Delphic Oracle's prophetic powers.)  NatGeo

The opening of The Eumenides offers its own genealogy of the site, beginning with the striking description of the Earth as πρωτόμαντιν - the first prophet:


πρῶτον μὲν εὐχῇ τῇδε πρεσβεύω θεῶν 
τὴν πρωτόμαντιν Γαῖαν: ἐκ δὲ τῆς Θέμιν, 
ἣ δὴ τὸ μητρὸς δευτέρα τόδ᾽ ἕζετο 
μαντεῖον, ὡς λόγος τις: ἐν δὲ τῷ τρίτῳ 
5λάχει, θελούσης, οὐδὲ πρὸς βίαν τινός, 
Τιτανὶς ἄλλη παῖς Χθονὸς καθέζετο, 
Φοίβη: δίδωσι δ᾽ ἣ γενέθλιον δόσιν 
Φοίβῳ: τὸ Φοίβης δ᾽ ὄνομ᾽ ἔχει παρώνυμον. 
λιπὼν δὲ λίμνην Δηλίαν τε χοιράδα, 
10κέλσας ἐπ᾽ ἀκτὰς ναυπόρους τὰς Παλλάδος, 
ἐς τήνδε γαῖαν ἦλθε Παρνησοῦ θ᾽ ἕδρας. 
πέμπουσι δ᾽ αὐτὸν καὶ σεβίζουσιν μέγα 
κελευθοποιοὶ παῖδες Ἡφαίστου, χθόνα 
ἀνήμερον τιθέντες ἡμερωμένην. 
15μολόντα δ᾽ αὐτὸν κάρτα τιμαλφεῖ λεώς, 
Δελφός τε χώρας τῆσδε πρυμνήτης ἄναξ. 
τέχνης δέ νιν Ζεὺς ἔνθεον κτίσας φρένα 
ἵζει τέταρτον τοῖσδε μάντιν ἐν θρόνοις: 
Διὸς προφήτης δ᾽ ἐστὶ Λοξίας πατρός. 

The Priestess of Pythian Apollo

First, in this prayer of mine, I give the place of highest honor among the gods to the first prophet, Earth; and after her to Themis, for she was the second to take this oracular seat of her mother, as legend tells. And in the third allotment, with Themis' consent and not by force, [5] another Titan, child of Earth, Phoebe, took her seat here. She gave it as a birthday gift to Phoebus, who has his name from Phoebe. Leaving the lake¹and ridge of Delos, he landed on Pallas' ship-frequented shores, [10] and came to this region and the dwelling places on Parnassus. The children of Hephaistos,²road-builders taming the wildness of the untamed land, escorted him with mighty reverence. And at his arrival, the people [15] and Delphus, helmsman and lord of this land, made a great celebration for him. Zeus inspired his heart with prophetic skill and established him as the fourth prophet on this throne; but Loxias is the spokesman of Zeus, his father.


Another article offers Some prophecies of the oracle

Xenocleia's tripod

The stories about Heracles are so various and numerous as to dwarf all other heroes. The tale of Xenocleia, linked to the murder of Iphitos and the mandatory service to Omphale, is worth a look:

Xenoclea, who appears as a character in the legend of Hercules, was the Pythia, or priestess and oracle, of the temple of Apollo at Delphi.
The Delphic oracle was a historical reality and was established in the 8th century BC. 

According to Pausanias and others, Hercules travelled to Delphi to consult the Oracle following the death of Iphitus, whom he had thrown off a wall in the city of Tiryns while Iphitus was staying with him as a guest. Suffering from nightmares, Hercules sought advice as to how to be cured. However, when he came to address his request to Xenoclea, she refused to help him, considering that he was still unpurified from the blood and death of Iphitus and also being shocked by the nature of his crime. Her only answer to him was "You murdered your guest, I have no oracle for such as you".  

This contemptuous reply so enraged Hercules that he sacrilegiously seized the priestess's Delphic tripod, took it away, and would not return it until she had agreed to grant his own request.

After the return of her tripod, and after bathing in the Castalian Spring, Xenoclea pronounced that Hercules would be purified of the death of Iphitus only by serving a year as a slave, with the price he fetched going to the children of Iphitus as compensation for the loss of their father. Asked who was to buy him, Xenoclea replied that it would be Omphale, Queen of Lydia. Hercules accepted the guidance of the oracle and agreed to serve Omphale for one year. 

Ancient depictions of the incident in the temple survive. On one ancient vase, Hercules is shown carrying off the sacred tripod, while Apollo, holding a branch of laurel, struggles to recover it and Xenoclea, apparently terrified by the dispute, looks on from a window, awaiting the outcome.

Heracles is more than the brilliant hero of the labors. He struggles with gods, scares oracles, and destroys innocent humans, including his first wife and children. Yet he was the splendid, saving alternative to Achelous:

Deianira: But at last, to my joy, the glorious son of Zeus and Alcmena came and closed with him in combat and delivered me.

Apollo and Hercules struggling for possession of the tripod, with Artemis on the left helping her brother, and Athena, in the center, helping Hercules.