See The Oxford Annotated Apocrypha (1977); G. W. E. Nickelsburg, Jewish Literature Between the Bible and the Mishnah (1981).
In biblical literature, works outside an accepted canon of scripture. In modern usage the Apocrypha refers to ancient Jewish books that are not part of the Hebrew Bible but are considered canonical in Roman Catholicism and Eastern Orthodoxy. Among the various books included are Tobit, Judith, Baruch, and the Maccabees as well as Ecclesiasticus and the Wisdom of Solomon. Protestant churches follow Jewish tradition in judging these works apocryphal or noncanonical. The term deuterocanonical is used to refer to works accepted in one canon but not all. Pseudepigrapha are spurious works for which biblical authorship is claimed.
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When used in the specific context of Judeo-Christian theology, the term apocrypha refers to any collection of scriptural texts that falls outside the canon. Given that different denominations have different ideas about what constitutes canonical scripture, there are several different versions of the apocrypha. During sixteenth-century controversies over the biblical canon the word "apocrypha" acquired a negative connotation, and it has become a synonym for "spurious" or "false". This usage usually involves fictitious or legendary accounts that are plausible enough to commonly be considered as truth. For example, Laozi's alleged authorship of the Tao Te Ching, Napolean Bonaparte's self-coronation rather than at the hands of Pope Pius VII, and the Parson Weems account of George Washington and the cherry tree, are all considered apocryphal.
"Concerning these scriptures, which are called apocryphal, for the reason that many things are found in them corrupt and against the true faith handed down by the elders, it has pleased them that they not be given a place nor be admitted to authority." (Translation by a Wikipedia editor.)
In practice, Jerome treated some books outside the Hebrew canon as if they were canonical, and the Western Church did not accept Jerome's definition of apocrypha, instead retaining the word's prior meaning (see: Deuterocanon). As a result, various church authorities labeled different books as apocrypha, treating them with varying levels of regard. Some apocryphal books were included in the Septuagint with little distinction made between them and the rest of the Old Testament. Origen, Clement and others cited some apocryphal books as "scripture", "divine scripture", "inspired", and the like. On the other hand, teachers connected with Palestine and familiar with the Hebrew canon excluded from the canon all of the Old Testament not found there. This view is reflected in the canon of Melito of Sardis, and in the prefaces and letters of Jerome
A third view was that the books were not as valuable as the canonical scriptures of the Hebrew collection, but were of value for moral uses, as introductory texts for new converts from paganism, and to be read in congregations. They were referred to as "ecclesiastical" works by Rufinus
These three opinions regarding the apocryphal books prevailed until the Protestant Reformation, when the idea of what constitutes canon became a matter of primary concern for Roman Catholics and Protestants alike. In 1546 the Catholic Council of Trent reconfirmed the canon of Augustine, dating to the second and third centuries, declaring "He is also to be anathema who does not receive these entire books, with all their parts, as they have been accustomed to be read in the Catholic Church, and are found in the ancient editions of the Latin Vulgate, as sacred and canonical." The whole of the books in question, with the exception of 1st and 2nd Esdras and the Prayer of Manasses, were declared canonical at Trent
The Protestants, in comparison, universally held the belief that only the books in the Hebrew collection were canonical. John Wycliffe, a 14th century reformer, had declared in his Biblical translation that "whatever book is in the Old Testament besides these twenty-five shall be set among the apocrypha, that is, without authority or belief"
Nevertheless, his translation of the Bible included the apocrypha and the Epistle of the Loadiceans.
The respect accorded to apocryphal books varied between Protestant denominations. In both the German (1537) and English (1535) translations of the Bible, the apocrypha are published in a separate section from the other books, although the Lutheran and Anglican lists are different. In some editions, (like the Westminster), readers were warned that these books were not "to be any otherwise approved or made use of than other human writings." A milder distinction was expressed elsewhere, such as in the "argument" introducing them in the Geneva Bible, and in the Sixth Article of the Church of England, where it is said that "the other books the church doth read for example of life and instruction of manners," though not to establish doctrine 
According to The Apocrypha, Bridge of the Testaments at orthodoxanglican.net:
(making most of the presently accepted canon, both Jewish and Christian, apocryphal in their eyes). Certain circles in Judaism, such as the Essenes in Judea and the Therapeutae in Egypt, were said to have a secret literature (see Dead Sea scrolls). Other traditions maintained different customs regarding canonicity
The Ethiopic Jews, for instance, seem to have retained a spread of canonical texts similar to the Ethiopian Orthodox Christians
, cf Encyclopedia Judaica, Vol 6, p 1147. A large part of this literature consisted of the apocalypses. Based on prophecies, these apocalyptic books were not considered scripture by all, but rather part of a literary form that flourished from 200 BC to AD 100.
Slightly varying collections of additional Books (called deuterocanonical by the Roman Catholic Church) form part of the Roman Catholic, Eastern Orthodox and Oriental Orthodox canons.
The Book of Enoch is included in the biblical canon only of the Oriental Orthodox churches of Ethiopia and Eritrea. However, the Epistle of Jude quotes the prophet, Enoch, by name, and some believe the use of this book appears in the four gospels and 1 Peter. The genuineness and inspiration of Enoch were believed in by the writer of the Epistle of Barnabas, Irenaeus, Tertullian and Clement of Alexandria, and much of the early church. The epistles of Paul and the gospels also show influences from the Book of Jubilees, which is part of the Ethiopian canon, as well as the Assumption of Moses and the Testaments of the Twelve Patriarchs, which are included in no biblical canon.
The high position which some apocryphal books occupied in the first two centuries was undermined by a variety of influences in the Christian church. All claims to the possession of a secret tradition (as held by many Gnostic sects) were denied by the influential theologians like Irenaeus and Tertullian, the timeframe of true inspiration was limited to the apostolic age, and universal acceptance by the church was required as proof of apostolic authorship. As these principles gained currency, books deemed apocryphal tended to become regarded as spurious and heretical writings, though books now considered deuterocanonical have been used in liturgy and theology from the first century to the present.
The Gnostic tradition was a prolific source of apocryphal gospels. While these writings borrowed the characteristic poetic features of apocalyptic literature from Judaism, Gnostic sects largely insisted on allegorical interpretations based on a secret apostolic tradition. With them, as with most Christians of the first and second centuries, apocryphal books were highly esteemed. A well-known Gnostic apocryphal book is the Gospel of Thomas, the only complete text of which was found in the Egyptian town of Nag Hammadi in 1945. The Gospel of Judas, a Gnostic gospel, also received much media attention when it was reconstructed in 2006.
Roman Catholics and Orthodox Christians as well as Protestants generally agree on the canon of the New Testament. However there is one notable exception. The Ethiopian Orthodox have in the past also included I & II Clement, and Shepherd of Hermas in their New Testament canon. This is no longer the case. The Ethiopian Orthodox canon also places the General Epistle of St. James immediately before the General Epistle of St. Jude.
Information concerning the Hellenist Jews was incorporated from the Catholic Encyclopedia at newadvent.com.