It’s perhaps the trickiest phrase (at least language-wise) in the Lord’s Prayer:

τὸν ἄρτον ἡμῶν τὸν ἐπιούσιον δὸς ἡμῖν σήμερον  (Mt 6:11.)

And what on earth does ἐπιούσιον mean? It’s not at all helped by the fact that this word only turns up in texts here, and then in commentaries on this text by later Greek-writing authors. That’s not to say that Jesus or the gospel writers coined it, just that here’s the first and really only place it’s used as an adjective.

The commentators offer up three main positions:

1. That it forms from ἐπί + οὐσία, very woodenly ‘upon’ + ‘substance’. That’s where Latin versions ended up with supersubstantialem which is at least equally, if not more, opaque, and very liable to heading down a transubstantion line of thinking. But more concretely it would/could still mean “for [our] subsistence”
2. That it comes from ἐπί + οὖσα (εἶναι “to be”), with ‘day’ understood. That it, it’s bread “for the day that is”, from which we get the regular translation “today’s bread”.
3. That it comes from ἐπί + οὖσα but from “to go” (ἰέναι) rather than “to be”, again with ‘day’ understood. So then it’s ‘the day that is coming’.

That third usage is found with the participle ἐπιούση which is found in Acts 7.26, 16.11, 20.15, and 21.18, in all four instances referring to the oncoming day (with the word ‘day’ omitted in three of these four instances). It’s very difficult though to decide on strict language grounds which of these explanations is the best for the situation, although on semantic grounds they tend to converge in meaning and seem to be borne out by, e.g. Syriac and Latin (just not Jerome) translations.

Whether ἐπιούση would refer to tomorrow or today of course depends on when you say it – in the evening or night, or even morning, it likely refers to the coming day; in the daytime itself, to the following day. In either case though we are talking about a socio-historical setting in which material needs and the provision of food generally took place on a day-to-day basis, so that getting the oncoming day’s food is a pressing concern. Hence my suggestion for a slightly different translation, “bread for the oncoming day”, which sidesteps whether it’s today or tomorrow, but keeps the sense of immediate need for bread each day, day by day.