There are three Eroses in Greek literature and they are not developments of one another so much as rivals.
Hesiod's: one of the first things that existed
In the Theogony, after Chaos and Earth and Tartarus, comes Eros — "most beautiful among the immortal gods, loosener of limbs, who overpowers the mind and sensible thought in the breasts of all gods and all men". He has no parents. He precedes Aphrodite by several generations and precedes almost everything else. He is not a god of romance; he is the force that makes anything join with anything, and without him the genealogies that fill the rest of the poem cannot start.
Aristophanes, in the Birds, gives a comic cosmogony in the same key: black-winged Night lays a wind-egg in the boundless bosom of Erebus, and from it hatches Eros with golden wings, who mates with Chaos and produces the race of birds. Orphic cosmogonies use a similar figure under the name Phanes or Protogonos, born from a cosmic egg, shining and bisexual, the first-born of everything.
Plato's: the philosophical middle term
The Symposium stages the disagreement explicitly. Speaker after speaker gives an account of him, and Socrates — reporting the priestess Diotima — argues against the whole company that Eros is not a god at all but a daimon, an intermediate being, the child of Poros (resource) and Penia (poverty), conceived at Aphrodite's birthday party. He is therefore permanently in want, permanently scheming, barefoot and homeless, and always pursuing what he lacks. Desire, in this account, is defined by not having.
That single passage produced the entire tradition of "Platonic love", the ladder from the beauty of one body to the beauty of institutions to beauty itself — and, as usually happens, the popular sense of the phrase has drifted a long way from the argument.
The Hellenistic: the boy with the arrows
By the third century BCE the cosmic power has become a small winged child, son of Aphrodite, mischievous and dangerous in a domestic way. Apollonius' Argonautica has the most memorable scene: Aphrodite finds him in Olympus playing knucklebones with Ganymede and cheating, and bribes him with a beautiful ball to shoot Medea — which he does, and the whole tragedy of Medea and Jason follows from a boy being paid in a toy.
The arrows come with this version, and the two kinds of arrow, gold to kindle love and lead to repel it, are Ovid's contribution in Metamorphoses 1, where they are used on Apollo and Daphne. Ovid also gives the motive: Cupid is annoyed at being teased about his little bow.
The plural also appears — Erotes, a flock of winged boys — which is why Hellenistic and Roman art is full of them and why they multiplied so easily into Renaissance putti.
Eros and Psyche
The one full narrative he has is late and is not Greek. It survives inside a comic novel — Apuleius wrote his Metamorphoses, the book everyone now calls The Golden Ass, in second-century Latin — and it arrives there at two removes, as a story an old woman tells to console a kidnapped girl. Its heroine is Psyche, whose name simply means "soul". A mortal princess so beautiful that Venus is neglected; Cupid sent to ruin her and falling in love instead; a husband who visits only in darkness and forbids her to look; the lamp, the drop of hot oil, the flight; the four impossible tasks set by Venus, including a descent to the underworld for a box of Proserpina's beauty; and a reconciliation on Olympus at which Psyche is made immortal and their child is named Pleasure.
It is the earliest full "animal bridegroom" tale in European literature — the structural ancestor of Beauty and the Beast and of the Norwegian East of the Sun and West of the Moon — and it has been read as allegory since antiquity, with the soul suffering, transgressing and finally being united with divine love. Whether Apuleius invented it or adapted an existing folk tale is not settled; the story's shape has good comparative parallels and no earlier Greek attestation. It is treated in full at the account of the tale.
Cult, and Thespiae
He was worshipped, and not only as a decorative figure. At Thespiae in Boeotia, at the foot of Helicon, Pausanias reports that the oldest cult image of Eros was an unworked stone, and that the city held a festival, the Erotidia, with athletic and musical contests every fifth year. Praxiteles' statue of Eros there was famous enough to be looted twice by Roman emperors. At Athens he had an altar at the entrance to the Academy and was worshipped alongside Anteros — "love returned" — on the north slope of the Acropolis. Sparta and Crete are reported to have sacrificed to him before battle, on the reasoning that an army's cohesion depended on the bonds between men in the line.
Cupid, Valentine's Day, and the loss of a cosmic force
The Roman Cupid (from cupido, desire) and Amor absorb the Hellenistic version and pass it to the Middle Ages, where the blindfolded Love who shoots at random becomes a stock allegorical figure — the blindfold is medieval, not ancient, and carries a moral judgement the Greeks did not make. From there he goes to Renaissance putti, to Caravaggio's insolent Amor Vincit Omnia, to Bouguereau, to the greetings-card cherub, to the pierced heart on a Valentine.
What has vanished entirely is Hesiod's. The primordial power that makes the universe capable of combination is now a chubby infant with a toy bow, which is possibly the single steepest demotion in the history of the Greek pantheon.
Contested parents, a rival brother, and a word that outlived him
Who are his parents?
Pick a source. Hesiod: nobody, he is primordial. Simonides: Aphrodite and Ares. Sappho: Aphrodite and Ouranos. Alcaeus: Iris and Zephyrus. Plato's Diotima: Poros and Penia. Later standard usage: Aphrodite, with the father unspecified or Ares. Cicero lists three different Cupids with different parents to make sense of the mess. The variety is not confusion in the sources so much as evidence that "Eros" names an idea that different poets attached to different genealogies.
What is Anteros?
A separate god, "love in return", said to punish those who do not requite affection. In one story he is given to Aphrodite as a companion for Eros because a child needs a playmate to grow. The statue on the Shaftesbury Memorial Fountain in Piccadilly Circus, universally called Eros, was in fact intended by its sculptor Alfred Gilbert as Anteros, representing selfless rather than erotic love — a distinction that lasted about five minutes after it was unveiled in 1893.
Why is he sometimes an adult?
Archaic and early classical art shows him as a beautiful youth, not a child — winged, athletic, sometimes with a lyre or a flower, appropriate to a god associated with the gymnasium and with the courtship customs of adult men and adolescents. The infantilisation is Hellenistic. If a vase looks too old for a chubby Cupid, that is because it is.
Does the word survive in English?
Extensively, and mostly through nineteenth- and twentieth-century usage rather than direct inheritance: erotic, eroticism, and — via Freud, who took the Platonic and Hesiodic senses seriously — Eros as the life drive opposed to Thanatos. Freud's pairing of the two names is his own construction, but he chose them knowing that both were real Greek deities and that one of them was a cosmic principle.