According to Hesiod, Achelous and all the other river-gods were sons of the Titans Oceanus and Tethys. The sixth-century mythographer Acusilaus called Achelous the "oldest and most honoured" of Oceanus's river-god offspring. One tradition, reported by Servius, held instead that Achelous was the son of Earth (Gaia).

Achelous fathered the Sirens, though the identity of their mother varies across sources, being attributed variously to an unnamed "melodious mother," the Muses Terpsichore or Melpomene, or the Calydonian princess Sterope. By Perimede, daughter of Aeolus, he fathered Hippodamas and Orestes.

He was also credited as the father of several nymphs associated with famous springs: Pirene at Corinth, Castalia at Delphi, Dirce at Thebes, and Callirrhoe ("the lovely spring"), who later became the wife of Alcmaeon. Plato and the poet Panyassis referred to "the nymphs" or "Achelesian nymphs" as his daughters, suggesting a tradition that Achelous fathered all springs, or at least their associated nymphs.

Achelous was a suitor for Deianeira, daughter of King Oeneus of Calydon. He transformed himself into a bull and fought Heracles for the right to marry her, but was defeated, and Heracles wed Deianeira. The story appeared as early as the 7th century BC in a now-lost poem by Archilochus. According to a summary of a lost Pindar poem, Heracles broke off one of Achelous's bull-horns during the contest, and the river-god recovered it by trading it for a horn from Amalthea.

In Sophocles' Women of Trachis, Deianeira describes how Achelous wooed her in three shapes: a bull, a serpent, and a half-man/half-bull creature with fountain-water spraying from his beard. Ovid's Metamorphoses offers a different version in which Achelous loses three times — first in human form, then as a snake, finally as a bull. Heracles tore off his bull-horn, and the Naiads filled it with fruit and flowers, creating the Horn of Plenty (cornucopia). In Hyginus's account the horn passes to the Hesperides (or Nymphs), while Strabo reports versions in which Heracles gives it to Deianeira's father Oeneus as a wedding present. The fourth-century rhetor Libanius even said the Sirens were born from the blood Achelous shed when his horn was broken.

Ancient writers also rationalized the myth as Heracles diverting the Achelous River's course: Diodorus Siculus and Strabo recount how, by confining the river with embankments and channels, Heracles defeated it and created fertile delta land — the legendary horn of plenty. Joseph Fontenrose suggested the story might reflect an ancient tradition of conflict between Zeus and Achelous.

Achelous also played a role in the story of the Argive hero Alcmaeon, who killed his mother Eriphyle and required purification. After long travels he reached the springs of the Achelous River, where the river-god purified him and gave him his daughter Callirrhoe as wife; at the river's mouth Alcmaeon found newly formed land, created by silt, where he could live free of his curse. Apollodorus adds that Achelous commanded Alcmaeon to dedicate the Necklace of Harmonia and the robe at Delphi.

In Ovid's Metamorphoses, Achelous appears in two transformation narratives about island creation near the river's mouth. The Echinades Islands were once five nymphs who, sacrificing on his banks, forgot to include Achelous; enraged, he flooded the land and swept them into the sea, where the ground cleft into the islands. He also describes saving Perimele, daughter of Hippodamas, whom her father threw from a cliff into the sea: Achelous prayed to Poseidon, who transformed her into an island.

Achelous's name could refer to water in general. Euripides describes a house being sprinkled with "Achelous' water" and servants bringing Achelous "to douse a fire," and in Aristophanes' Lysistrata a chorus leader cries "Achelous, you're on!" while pouring water.

The name specifically referenced water mixed with wine for drinking. A Sophocles fragment runs, "So Achelous runs with wine in our place"; a satyr play by Achaeus shows satyrs complaining about too much "of Achelous" being mixed into their wine; and an Aristophanes fragment describes a sufferer who drank unwatered wine "having no admixture of Achelous." In Ovid's Fasti and in Virgil the name stands in for water mixed with wine, and Hyginus reports that a man named Cerasus first mixed wine with "the Achelous river in Aetolia," explaining the Greek word for mixing, cerasai.

Achelous is mythologically linked with Dionysus and wine through Deianeira and her father Oeneus, whose name means "Wine-man." Apollodorus states Oeneus was the first mortal given the grape vine by Dionysus, and Hyginus explains he received the vine as a reward for tolerating Dionysus's seduction of his wife and fathering of Deianeira.

Achelous was a rural-agricultural water deity whose importance reflected the agricultural significance of rivers and fertile deltas, a connection reinforced by his broken horn's association with the cornucopia. Some Greeks apparently considered sacrifices to Achelous more important than those to the grain-goddess Demeter, since Acheloios was the name of all rivers "and the crop comes from water." Many inscriptions attest his cult, particularly associated with the oracle at Dodona, though it declined from the late fourth century BC onward.

From at least Homer's time Achelous was an important divinity throughout Greece. Homer called him "king" and used him to measure Zeus's superior strength: "With Zeus doth not even king Achelous vie, nor the great might of deep-flowing Ocean, from whom all rivers flow and every sea." Some ancient scholars considered the line about Oceanus spurious, which would make Achelous himself the source of all waters, aligning with Acusilaus's assessment and with epic fragments calling rivers the "sinews of Achelous."

Achelous appears as a cultic figure as early as the seventh century BC; Pausanias reports an altar to him near Megara erected by the tyrant Theagenes, and Achelous was the only river-god to achieve Panhellenic cult status, often sharing sanctuaries with his daughter-nymphs. He appears in many votive reliefs, frequently with nymphs, and was venerated in the form of stylized votive masks similar to those of Dionysus, such as a marble mask from Marathon (c. 490–470 BC). According to Ephorus, the Dodona oracle regularly commanded sacrifices to Achelous, and his name was frequently invoked in oaths, prayers, and sacrifices; Plato's Phaedrus places a shrine "of some nymphs and of Achelous" along the Ilissus.

Achelous's appearance as a bull in his contest with Heracles reflects a Greek tradition — perhaps as old as Homer or older — associating rivers and river-gods with bulls. Strabo reports that some claimed the Achelous, like other rivers, was called "like a bull" from the roaring of its waters and from the bendings of its streams, which were called Horns.

This association is reflected in Greek depictions of river-gods as part bull from at least the Archaic period onward, and an ancient connection between horns and the fertility that rivers provide is evident in the horn-of-plenty narrative.

Achelous was a popular subject in ancient Greek art, with over twenty surviving examples of his fight with Heracles in Attic vase painting alone, besides many votive reliefs alongside other divinities. Where inscriptions confirm his identity he characteristically appears as a "man-bull" — a bull with a bull-horned and bull-eared human face, head, or torso with a bison-like beard — in full figure or abbreviated as a torso, head, or mask. He appears much more rarely in human form alone, and was also common in Etruscan art; his man-bull iconography probably derived from oriental art.

His contest with Heracles was depicted from the second quarter of the sixth century BC onward, usually with Heracles grabbing the single horn. The possibly earliest version (c. 600–560 BC) on a Middle Corinthian kylix shows a horned centaur-like Achelous; the earliest Attic versions show a bull with a man's head and beard. A red-figure stamnos attributed to Oltos (British Museum E437) shows Achelous with a bearded human torso on a long serpentine, fish-tailed body, while a column krater in the Louvre shows his broken horn on the ground as Heracles threatens him with a club. Pausanias saw the scene on the throne of Amyclae and in the Megarian Treasury at Olympia.

From the late fifth century BC, Achelous appears in many votive reliefs, often with his daughter-nymphs, frequently in cave-form scenes led by Hermes or Pan, with Achelous carved into the cave wall. Unaccompanied man-bull images — inferred to be Achelous where inscriptions are lacking — are even more frequent, appearing on coins of cities in Magna Graecia and Sicily, as well as on gems, jewelry, bronzes, and architectural terracottas.

The Achelous River rises in the Pindus mountains and flows into the Ionian Sea near the Echinades Islands in western Greece, dividing ancient Acarnania and Aetolia. Servius offers one origin story in which Achelous, son of Earth, grieved the loss of his daughter-Sirens and was received into his mother's bosom, whereupon Earth caused a river bearing his name to gush forth. Pseudo-Plutarch reports that the river was formerly called Thestius, and Strabo that "earlier times" called it the Thoas; Strabo notes it was likened to a bull from its roaring and meanders and to a serpent from its length and winding turns.

Achelous was a common river name in antiquity. Besides "king Achelous," Homer apparently knew of an Achelous river in Lydia near Mount Sipylos, Strabo mentions two more (one in Achaea near Dyme, another in Thessaly near Lamia), and Pausanias notes a tributary of the Alpheius in Arcadia. The multiplicity of same-named rivers, perhaps due to the river-god's equation with water, has been taken to suggest that Achelous may originally have been the primal source of all water.