I can only really speak for the development of the New Testament canon, rather than the compilation of the Old, which was more or less delineated, at least for the Greek-speaking world, as those texts belonging to the famous Septuagint edition (although it was certainly a bit more flexible, as you'll find Jews and Christians quoting other books as Jewish Scriptures, e.g. the Epistle of Jude, which is in the New Testament, quotes from 1 Enoch).

It is absolutely crucial to recall that, for the first century or so, Christian "Scripture" designated strictly the books of the Old Testament. For the primitive Church, “books other than the Hebrew Bible or its Septuagint version played a negligible part in the initial propagation of the faith” (Chadwick p. 43), as can be seen in the way New Testament texts are treated by the Apostolic Fathers. It is worth noting how this new body of Christian literature came to be elevated to the rank of Scripture, alongside its Jewish antecedent. In 1 Clement, all Old Testament quotations are prefaced with the formulaic “it is written” or “Scripture says”, whereas none of his relatively impoverished New Testament quotes receive the same accolades, indicating that he did not quite see them as fully fledged scripture. The same is true of Ignatius, though we see that he begins to put a bit more of an emphasis on a “new” authority, delineating the “archives” of the Hebrew Scriptures and Christ with the “Gospel” (e.g. Ignatius, Smyrn. 5.1). In Polycarp, this changing attitude is similarly evident, where he quotes (in his extant epistle) New Testament writings around one hundred times, with only around a dozen from the Septuagint. A later dating of 2 Peter would place it around this period, and it reflects the gradual ‘scripturalization’ of some New Testament writings, as it seems to put Paul’s epistles on a level with the other scriptures (cf 2 Pet 3.15f). 2 Clement (not authentic, but dating also from the opening of the 2nd century) marks a significant turning point in quoting Matthew with “Another Scripture says…” Kinzig (p. 536) argues that this burgeoning awareness of a new, “Christian” set of scriptures was first delineated as the “New Testament” by Marcion—fittingly, as he (as if engaged in amputation) sharply distinguished between the Gospel and the Old, Jewish Scriptures—and this appellation was adapted later by the orthodox. With Irenaeus, “the fully scriptural character of the specifically Christian writings was universally acknowledged, and the description of them as the ‘New Testament’…came into vogue” (Kelly p. 56). To nuance the understanding of Scripture further, it cannot be taken simply to mean texts that are true and authoritative, but implies (as will be discussed later) apostolicity, and on this basis 1 Clement, Hermas, and others were pushed outside of the canon. Tellingly, we can see Tertullian place great authority on the Sibylline oracles (alongside Commodian and Theophilus), for the Sibyl “was a prophetess of the true God”, but this deference cannot be said to indicate that they were regarded as scriptural, only authoritative and useful. By Tertullian, there is fully recognized a twofold collection of equal authority, both equally “divine scripture.” This understanding, by the beginning of the 3rd century, had already well-permeated Christendom and gained universal sanction, where it become normative to speak of “a fresh, new Testament.” (Clem. Paed. I.59.1).

Furthermore, The Apostolic and sub-Apostolic ages did not overly concern themselves with the spreading of the recent buds of New Testament literature, having still fresh in mind the apostles and the oral gospel tradition. Papias does not flinch to prefer the oral to the written, saying that he “did not think that information from books would help so much as the word of a living and abiding voice” (quoted in Eusebius, H.E. III.39.4). Clement of Rome, a the close of the first century, could still remind his readers to “remember the words of the Lord Jesus” (1 Clem. xiii.2), and cite quite freely from an oral cache of Jesus’ sayings. As is the nature of oral tradition, it is uniquely prone to enlargement and mythologization, and we can see in the days of Papias fantastical tales circulating of Judas swelling to a monstrous size before dying publicly. As oral tradition grew expired and distorted, a reliance on written texts developed, particularly the gospels. Clement’s letter to the Corinthians indicates that they had copies of Paul’s letters to the Romans (ca. 95 AD), indicating that New Testament literature was beginning to be preserved and cultivated across Christendom. Relatedly, Clement demonstrates a significant acquaintance with Paul’s epistles, showing the same was true of the Roman church. Paul’s letters began to be assembled according to the seven-church format (perhaps echoing Revelations) and the 14-letter format in use today was current by Origen. By 150 we find Justin Martyr familiar with all four gospels (‘the memoirs of the apostles’, 1 Apol. 66), who began also to quote New Testament writings with the scriptural stamp of “it is written” (e.g. Justin Martyr, Dial. 49.5). Irenaeus was the first to explicitly frame a “fourfold gospel”, and he began to preface them similarly with “scriptura ait” (Haer. III.11.8), something that he did not, interestingly, perform for quotations from Paul. As is evident from Luke’s preface, “the trend toward a multiplicity of Gospels existed from the very beginning”, and the early Church did not particularly struggle over there being four evangelists. That being said, evidence suggests that most primitive churches used only one Gospel, for of all the codices of the first half of the second century, they only contained one, rather than several, gospels. Besides “the four”, many different gospel traditions emerged, some proto-orthodox (as in the Gospel of the Hebrews), and many gnostic ones (as per the Valentinian “Gospel of Truth”). Irenaeus says of the Gnostics that they “boast that they possess more gospels than there really are”, wherein “they also introduce secrets of the apocrypha (arcana apocryphorum), the inventions of blasphemy.” Here, then, can be found a growing interest in cultivating a collection of Christian literature to gradually replace the dying oral tradition, and with it, a keen desire to get the “right” books for such a task.

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