"Who wrote the Epistle to the Hebrews? In truth, God knows." So wrote Origen of Alexandria in the third century, and his verdict stands. The letter is anonymous — the attribution to Paul, which appears in some manuscript traditions and was accepted in the East, was always doubted in the West and is rejected by virtually all modern scholars. The Greek is too polished, the theology too different, the rhetorical strategy too sophisticated to be Paul's.
The author was clearly a highly educated Greek-speaking Christian, trained in rhetoric and deeply versed in the Septuagint (the Greek translation of the Hebrew scriptures), which serves as the basis for the letter's elaborate typological arguments. Various candidates have been proposed over the centuries: Barnabas (Tertullian's suggestion), Apollos (Luther's inspired guess, which has much to commend it), Clement of Rome, Priscilla, and others.
Whoever wrote it produced a masterpiece. Hebrews is not really a letter but a sermon — the author calls it a "word of exhortation" (13:22) — and it is the most sustained piece of theological argument in the New Testament outside Paul's letters. Its central thesis is that Christ is the ultimate high priest, whose self-sacrifice supersedes and fulfils the entire sacrificial system of the Jewish Temple.
The prose style is magnificent: the periodic sentences of the opening paragraph (1:1–4), the roll-call of faith in chapter 11 ("By faith Abraham..."), and the exhortation to "run with perseverance the race marked out for us" (12:1) are among the finest passages in Koine Greek literature.
The letter is usually dated to the 60s or 80s CE. Its audience appears to be a community of Jewish Christians in danger of abandoning their faith — the warnings against apostasy are the most severe in the New Testament.