This is another place where it would be really quick if I stuck to Hesiod's description which is as follows:
θεία δ᾽ Ἠέλιόν τε μέγαν λαμπράν τε Σελήνην
Ἠῶ θ᾽, ἣ πάντεσσιν ἐπιχθονίοισι φαείνει
ἀθανάτοις τε θεοῖσι, τοὶ οὐρανὸν εὐρὺν ἔχουσι,
γείναθ᾽ ὑποδμηθεῖσ᾽ Ὑπερίονος ἐν φιλότητι.
And Theia begot great Helios, bright Selene, and Eos (all shine on earth and are immortal gods, they have their home in the broad sky) having been overpowered in love by Hyperion.
 The sun
 The moon
 or "heaven" if you prefer.
 or whathaveyou the word can mean a lot of things. Seduced being the option I was originally going with. It could actually say that she tamed him for herself. One thing that is clear is that it really means love. The world translated as love does not just mean sex, it means love, affection, friendship. You have to go to the big dictionary (the Great Scott) to even get sex mentioned.
And furthermore, it could just mean that they married while in love. I might go with that.
So that's... not a lot.
Here we go:
Once upon a time there was only Khaos. Neither light nor dark, neither colored nor colorless, neither something nor nothing. In Khaos probability and possibility ruled, and there was no such thing as "is".
But from Chaos sprang Gaia, the solid foundation on which all is built.
Other gods sprang from Khaos. Misty Tartaros, who dwells within Gaia, in the empty space beneath her surface, Eros, who first brought gods together in love. Finally Erebos and Nyx, the first gods Eros brought together.
Nyx (night) brought darkness to the surface world while Erebos (the gloom of Tartaros) brought the same to to the subsurface, but their daughter Hemera (day) brought the first light to the surface and so the cycle of Night and day was born. But not night and day as we know them because there was not yet a sun, not yet a moon or stars. It simply was day when and where Hemera covered Gaia and was night when and where Nyx did.
Gaia, inspired by Nyx's example brought forth children of her own. Ouranos (the sky) mountains and islands (though they were not islands yet as there was no sea) and finally Pontos (the barren sea.)
Eros brought her together with Ouranos and the two had more children. First the ones who would later be known as the Titans: Okeanos, Koios, Krios, Hyperion, Iapetos, Rheia, Themis, Mnemosyne, Phoibe, Tethys and Khronos. Ouranos shoved her later children by him back inside of her, sealing them in misty Tartaros.
So Gaia came to her free children for help. Kronos overthrew Ouranos and made himself king of the universe and the other Titans lesser rulers of various subdomains, but he didn't free his trapped siblings.
Theia was given dominion over light and sight, while Hyperion was made a watcher and given dominion over observation.
The two loved each other and married. They had four children. Their first three included one son, Helios, the sun, and two daughters, Selene, the moon, and Eos, dawn. All three made their homes in the sky. Their youngest child, Titan, was given the name Ouranos had branded his parents with. He chose to dwell on the surface of Gaia.
Eos, along with the daughters of Nyx who were responsible for creating evening, completed the daily cycle of night, dawn, day, evening, and then night again.
Helios rose with his sister Eos, provided direction to the light of while Hemera covered the surface of Gaia, and set when seven of Nyx's daughters brought evening. He never intruded upon Nyx's domain.
Selene was more open to change than her brother. She changed her appearance, and she changed the times when she came out, feeling free to traverse the domains of dawn, day, evening, and night.
Helios mated with various people at various times. In no particular order [putting this in order is going to be hell, by the way. Not just Helios, I mean the whole thing] these are his mates and descendants:
Perseis, daughter of Okeanos and Tethys, bore Helios four children. Witches all. The female witches were Pasiphae and Kirke (who Odysseus once encountered) and the male witches were Aeetes and Perses.
Pasiphae married King Minos of Krete. Their children were Ariadne, Androgeus, Glaucus, Deucalion, Phaedra, and Katreus. Unfortunately for Pasiphae, Minos managed to piss of Poseidon, the story goes like this (more or less):
Minos was having some dispute about whether he should be king of Krete, and prayed that a perfect bull would appear as a sign he deserved the island nation, which he would then sacrifice to Poseidon. The bull did come, and was indeed perfect, but Minos was so impressed with its perfection that he kept it for himself and sacrificed on of his own herd to Poseidon in its place.
Poseidon noticed this, and was pissed off. But rather than attack Minos directly he decided to come after him sideways and so went to Aphrodite for help. Aphrodite made Pasiphae fall in love with the bull.
Some time after this Pasiphae could resist the love, which Aphrodite always couples with lust, no longer and went to Daedalus, the greatest inventor there was, to find a way for her to... uh, how do I put this? Have sex with the bull.
Daedalus created a fake cow in which she could disguise herself and some months later a child was born. His name was Asterion, which means starlike. Most of Greece didn't think part animal part human with the head of a bull was all that starlike. They called it the Minotaur (the bull of Minos.)
As the Asterion came of age Minos contracted Daedalus to construct the labyrinth in which to keep the beast.
Now Androgeos went to Athens to participate in games there, but after he won every single prize he was murdered by jealous Athenians. Eventually it came to pass that the gods demanded that the Athenians give Minos whatever he asked for as a means of reparation. What he asked for was a regular shipment of Athenian youths to feed to Asterion, the Minotaur.
Eventually Theseus, prince of Athens, went off as one of the youths intent on killing the Minotaur. This is a task he would have failed at utterly if he had not gotten help from one of Minos and Pasiphae's daughters, Ariadne.
But Theseus had promised not to take on a foriegn bride, so one day he stopped at the island of Naxos, slept with her on a bed he created on the shore, and then ran away before she could wake up.
At this point the furious, shocked, and distraught Ariadne ran out of hope. She knew she couldn't go home, even if she had a boat, and the likelihood of anyone else stopping on the island treating her fairly was low, if anyone else stopped on the island at all.
Then Dionysus came by, they hit it off, and got married. But, Ariadne being mortal, she eventually died. So Dionysus went down to the underworld, took her back, made her into a god, and they dwell together on Olympus to this day.
Those are the stories of Ariadne, Androgeus, and Asterion
The stories of Glaucus, Deucalion, Phaedra, and Katreus are left to be told.
Glaucus, while still a child , was playing with a ball one day. Some say he played with a ball and a mouse. That's not important, all that matters is that the ball ended up in a vat of honey and Glaucus, in trying to get it out, fell into the vat of honey. There he drowned.
Minos and Pasiphae looked all over for their son, but were not able to find him. Thus the journeyed to the Oracle at Delphi. She told the two that an incredible being had been born amoung them, whoever could explain it would also be able to return their son to them alive.
They returned to their land and discovered a young bull that changed color three times a day. None of their own soothsayers could explain it, but a traveling soothsayer named Polyidus (son of Coeranus) observed the bull. at the start of the day it would be white, later it would turn red, and by the end of the day it would be black. This much was known to all, but what Polyidus realized was that this was like the fruit of a mulberry tree, first white, then red, then finally when it is ripe, red.
Minos considered that a satisfactory explanation and assigned Polyidus the task of finding Glaucus. He observed many omens, but the only one that mattered was an owl who sat over the wine cellar and put bees to flight. Knowing that this was somehow significant and that the owl of Athena shared the same name as the missing boy, he was able to locate the dead Glaucus (and his ball) in the vat of honey.
Minos and Pasiphae were obviously not satisfied as they'd been promised the return of their son alive. Polyidus tried to explain that soothsayers lack the power to restore the dead to life, but Minos wasn't satisfied and locked Polyidus in the cellar with the body of Glaucus.
Now while soothsayers may lack the power to restore the dead to life serpents have no such limitations and so it was that a serpent was Polyidus' salvation.
A serpent entered the cellar through a hole of its own making and, on seeing the honey dipped corpse of Glaucus headed straight for it. Polyidus, trapped in the cellar with the serpent and the body quickly killed the serpent with his sword.
Soon afterward a second serpent came and restored the first to life with a special herb. Polyidus was able to steal some of the herb. Not much, but enough to revive the boy.
That secured his release from the wine cellar, but Minos demanded that he not return home until he taught Glaucus the art of soothsaying.
Polyidus did this, and did it to Minas' satisfaction, but before he left he made a strange request of Glaucus, he ordered that the boy spit in his mouth. This disgusting act caused the boy to forget all he had learned of soothsaying. Minos, for his part, accepted this well and when Polyidus returned home it was with many gifts in honor of him restoring Glaucus to life. Later, they say, Glaucus led a military expedition against Italy.
Phaedra married Theseus (yes, the same one who left her sister abandoned on a deserted island.) Katreus and Deucalion became kings of Krete, in that order, after Minos died.
Kirke, the second daughter of Helios and Perseis, made an island her home and was known for changing the men who came there into animals. A practice she continued, until Odysseus (with the help of Hermes) proved immune to her power. She was able to keep him on her island for a full year, and in that time became pregnant. She bore three children: Agrios, Latinos, and Telegonos.
She also mated with Poseidon and bore the minor god of forests, Phanos.
Aeetes, the first son, married the Okaniad Idyia, and became King of Kolchis. Most famous for possessing the Golden Fleece and then, you know, losing it. It was given to him by Phrixus in response to hospitality, and taken from him by Medeia, his daughter by Idyia, and Jason, son of Aeson.
Aeetes had other consorts as well. Before he met Idyia he mated with Asterodeia and she bore him the son, Apsyrtus. Who would be killed by Medeia with the help of Jason.
Chalciope, also a daughter of Aeetes and Idyia married Phrixus.
Perses, the second son, became king of the Persians. He deposed Aeetes, but was deposed by Medeia.
By the younger Klymene he fathered Phaeton, and then made the mistake of swearing by the river Styx that he would grant Phaeton a favor without knowing what that favor was. The favor was to drive Helios, the sun, across the sky. By this time Zeus was in charge and Apollo traditionally steered the sun, which was a largely ceremonial job as Helios had never had much trouble finding his own way through the sky.
But the horses did need to be directed as they were capable of pulling Helios around this way and that if they weren't.
The favor Phaeton asked for? To direct the horses.
He lost control, scorched parts of the earth, and some said he would have set the air itself aflame and boiled the seas if he hadn't been removed.
And so he was removed. Zeus from his seat of power on Olympus sent out a single lightning bolt. His aim was true, and Phaeton died before he knew what happened. With him out of the way, his desperate attempts to regain control no longer tugging them this way and that, the horses calmed down and Helios was able to salvage the situation, but not to save his son.
Helios and the younger Klymene also had a daughter, the nymph Astris who married the river Hydaspes and gave birth to Deriades, emperor or the Indians.
With Neaira he had two daughters, Lampetie and Phaethousa. Both tended the herds of Helios on the island of Thrinakie. Phaethousa tended seventy flocks of 50 sheep each, to control these 350 animals she used nothing more than a silver shepherds crook. Lampetie tended seven herds of 50 cattle each. To control them she used a simple copper staff.
These animals were ageless, their numbers never decreased by death or increased by birth. The simply lived well.
Until Odysseus came. His men slaughtered and ate many of the fine cattle of the sun. Lampetie was justifiably pissed off and ran to her father to tell him what had happened. As punishment for their crimes every single one of Odysseus's men were killed off. Odysseus himself did not die, for he had not participated in the crime, but he also did not escape punishment because he had failed to stop it in spite of being warned twice and theoretically in charge. Shipwrecked he washed onto Kalypso's island and spent the next seven years as the goddess' sex object.
That he is the father of the goddess Ikhnaie, tracing/tracking, is remembered. What no one remembers is who her mother was.
Aloeus, another son whose mother is forgotten, was the mortal king of Korinthos.
Nausidame, princess of Elis, bore Helios a son, Augeas, who became king of Elis.
Ocyrhoe bore to Helios a child about which nothing is remembered except that he was named for his uncle Phasis. This caused some confusion, as common names often do.
Leucothoe, a princess of Andros, bore to him Thersanon, one of the Argonauts.
Loving the Island of Rhodes produced the Heliaidai, the seven kings of Rhodes, as well as Elektryone, a princess of Rhodes.
That might be it for Helios.
* Anyone else have "I fell into a vat of chocolate" by the Smother's Brothers in their head?