His most famous quotation is perhaps

ποταμοῖσι τοῖσιν αὐτοῖσιν ἐμβαίνουσιν, ἕτερα καὶ ἕτερα ὕδατα ἐπιρρεῖ.
Potamoisi toisin autoisin embainousin, hetera kai hetera hudata epirrei
"On those stepping into rivers (staying the same), other and other waters flow on."

Herodotus's Greek words have a most mellifluous internal rhyme and rhythm -
oisi oisi oisi ousi, hetera hetera hudata.

In his Cratylus 402a, Plato much less poetically paraphrases Heraclitus's saying about rivers, and he uses χωρεῖ (gives way, make room) rather than ῥεῖ (flows).

πάντα χωρεῖ καὶ οὐδὲν μένει" καὶ δὶς ἐς τὸν αὐτὸν ποταμὸν οὐκ ἂν ἐμβαίης
Panta chōrei kai ouden menei kai dis es ton auton potamon ouk an embaies

The Loeb translation (H.N.Fowler) is "all things move and nothing remains still, and he likens the universe to the current of a river, saying that you cannot step twice into the same river."

In Cratylus 401d we find,

τὰ ὄντα ἰέναι τε πάντα καὶ μένειν οὐδέν
Ta onta ienai te panta kai menein ouden
"All things move and nothing remains still"

Heraclitus is said to have concluded rather dialectically that we both "step and do not step into the river, that we are and are not," sounding obscurely like the modern obscurant G.W.F.Hegel

ποταμοῖσ τοῖσ αὐτοῖσ ἐμβαίνομεν τε και οὐκ ἐμβαίνομεν, εἶμεν τε και οὐκεἶμεν. (Diels-Kranz B49a, "Homeric Questions.")

Heraclitus is also famous for saying that there is something that governs all this change, something which in itself is eternal. He called it "Logos." The modern interpretation is that he intuits the notion of laws of nature that describe the material world. Theologians have for centuries identified Heraclitus's logos with God.

In Aristotle's Rhetoric 1407b we find,

τοῦ λόγου τοῦδ᾽ ἐόντος ἀεὶ ἀξύνετοι ἄνθρωποι γίγνονται
Tou logou tous eontos aei
"the logos of all things is eternal"

Aristotle uses ἐόντος, the early Ionic form of ὂντος from Heraclitus's time and place.

Martin Heidegger translates τὰ ὄντα as das Seindes - "beings." He contrasts these "things that exist" with his Sein - "Being." Heidegger hoped to answer the "question of Being" by looking back before Aristotle, Plato, and Socrates to the "presocratic thinkers Anaximander, Heraclitus, andParmenides.

For Plato, "Being" is one of his forms or "ideas" that are prior to any instance of an object with a given form. The forms exist, or subsist, in another "realm" that is more "real" for Plato than the everyday physical world of material objects. Forms outside space and time resemble Immanuel Kant's noumenal world of the thing in-itself, the "Ding an sich.".

Plato set up the fundamental dualism of philosophy, the distinction between idealism and materialism, between abstract eternal essences and concrete ephemeral existences, between Parmenidean Being and Heraclitean Becoming

In Timaeus 27d, Plato asked "What is Being always, but has no Becoming (origin or genesis), and what is Becoming always, and never Being?"

τί τὸ ὂν ἀεί͵ γένεσιν δὲ οὐκ ἔχον͵ καὶ τί τὸ γιγνόμενον μὲν ἀεί͵ ὂν δὲ οὐδέποτε,

Plato preferred the "Being" (τὸ ὂν) of Parmenides over the "Becoming" (γιγνόμενον) of Heraclitus. That Being was from the earliest times associated with God may account for the survival of Plato's corpus and the demolition into fragments of the work of Heraclitus.