Historically, baptism has always been administered by the Christian Church – although not always in the same mode or with the same meaning. From the 1st century to the 16th century baptism was administered by immersion, pouring (affusion), and sprinkling. Baptism was administered to adult converts (especially in missional situations) and to children (especially in ecclesial situations).
Evidence for baptismal practices throughout Christian history is readily available. Evidence from the 1st century is found in the New Testament Scriptures. The Biblical Foundations of household baptism are discussed more fully in Part 2 of this series.
Evidence from the 2nd century suggests that baptism was administered to adult converts and their young children and infants. Christian Historian Philip Schaff offers incidental evidence for household baptism from AD 100-325:
Justin Martyr expressly teaches the capacity of all men for spiritual circumcision by baptism; and his “all” can with the less propriety be limited, since he is here speaking to a Jew. He also says that many old men and women of sixty and seventy years of age have been from childhood disciples of Christ. Polycarp was eighty-six years a Christian, and must have been baptized in early youth. According to Irenaeus, his pupil and a faithful bearer of Johannean tradition, Christ passed through all the stages of life, to sanctify them all, and came to redeem, through himself, “all who through him are born again unto God, sucklings, children, boys, youths, and adults.” This profound view seems to involve an acknowledgment not only of the idea of infant baptism, but also of the practice of it; for in the mind of Irenaeus and the ancient church baptism and regeneration were intimately connected and almost identified.
The Didache (a manual of Christian life and worship from the early 2nd century) indicates that baptism was to be performed for new converts in the triune name of God in running water, or standing water, in cold or warm water, either by immersion or by affusion.
Evidence from the 3rd century shows that baptism was administered to infants, converts, and whole households. The Apostolic Tradition of Hippolytus makes it clear that baptism was performed with water in the name of the triune God. In 21:3-5 baptismal candidates are instructed to come to the water at cockcrow
Then they shall remove their clothing. And first baptize the little ones; if they can speak for themselves they shall do so; if not, their parents or other relatives shall speak for them. Then baptize the men, and last of all the women.
Clearly, this shows that some form of household baptism was still practiced by the Christian church well into the 3rd century.
Between the 4th and 16th centuries, the culture of the Western civilization became more and more Christianized. As that happened the Christian church became more ecclesial and perhaps less missional. Therefore, as a result, infant baptism became the baptismal norm. Philip Schaff explains that prior to the 4th century,
[w]hile the church was still a missionary institution in the midst of a heathen world, infant baptism was overshadowed by the baptism of adult proselytes; as, in the following periods, upon the union of church and state, the order was reversed.
When the Christian church was adopted as the official religion of the Empire, baptism was administered more frequently in ecclesial contexts than in missional situations.
In the 16th century, during the Post-Reformation era, an alternative baptismal practice emerged. While the vast majority of professing Protestant Christians had retained some form of the historic Christian practice of household baptism (which included adults and children), the notorious Radical Reformers pushed for the baptism of adult believers only. They saw this as a corrective measure against what they considered to be the error of infant-baptism. The Radical Reformers sought to re-establish the primitive apostolic church according to the New Testament alone. In that sense they were more like restorationists than reformers. They were among the first “credobaptist-only” Christians in the history of the Church. They rejected infant-baptism as a legitimate practice, and required those baptized as infants to be “rebaptized” as adults.
The Radical Reformers sought to establish Christian faith and life on the New Testament only. That seemed plausible to some, but others realized that the apostles never intended that their writings should supplant the prophetic writings. Despite their desire and effort to restore apostolic Christianity, they failed to grasp that infant-baptism had its roots in the apostolic practice of household baptism.
Today, although biblical-theological and historical evidence clearly suggests that oikobaptism was a normative part of the apostolic practice of baptism, not all are convinced. To a large degree one’s view of covenant, household, and baptism is determined by one’s hermeneutic—the way one reads the Holy Scriptures.
Historical evidence shows that until the 4th century the primary Bible of the early Christian church was the Septuagint, a Greek translation of Hebrew Scriptures. The apostles’ writings were available and circulated among the churches from the 1st century on, but they were not formally collected and canonized until the 4th century. In the mean time, the early Christian church mainly read and studied the Hebrew Scriptures along side copies of the apostolic writings. Until the apostolic writings were formally canonized as Holy Scripture along with the prophetic writings, the Hebrew Scriptures were more accessible to the early church than were the apostolic writings—and they were just as authoritative for life and doctrine (Acts 15:21). So if the orthodox historic Christian church seems to have a “Jewish” (covenantal and liturgical) flavor it is probably due to the fact that her life and doctrine has been shaped by a “tota scriptura” reading of the Bible.
How does this connect to the discussion of baptism? It shows that oikobaptism was not grafted onto the scriptures synthetically, but rather grew out of them organically and covenantally.
The early Christian apologists and theologians took their hermeneutical cues from the apostles. By and large, they read the Holy Scriptures through a Christ-shaped lens (Rom 10:4). Admittedly, their interest in typology and allegory occasionally led them to over-spiritualize some texts, yet overall they tended to towards a “redemptive-historical” way of reading the Bible. Such an approach enabled them to acknowledge the deep unity and continuity between the prophetic writings and the apostolic writings, between the Hebrew Scriptures and the Christian Scriptures. Thus, they reasoned by the analogy of faith that baptism was a household affair. 
As mentioned above, from the 4th century to the 16th century Christian baptism was administered both to infants and children in ecclesial contexts and to adult converts and their children in missional contexts. The point here is that the formal canonization of the apostolic writings (i.e. the formation of the New Testament) did not eradicate, but rather established, the practice of covenant household baptism (which by definition includes both infant-baptism and believer-baptism).
Tragically, one of the unintended consequences of the Reformation experienced throughout the Christian community is that the one baptism instituted by the Lord Jesus Christ is now administered in diverse ways and for a variety of reasons—some biblical, some not.
Biblically, there is one baptism. Historically, the one baptism has been administered in various ways. Existentially, baptism is often detached from its covenantal roots, dislocated from the church, and centered on the individual rather than on Christ. What God gave the church as a sign of union with Christ and communion with the triune God and his saints has, in many places, devolved into a mark of division and schism.
To reverse this downward trend the Christian church must recover the biblical-theological and historical practice of oikobaptism. That requires a re-discovery of the biblical-theological themes of covenant, household, and baptism.
Next: Pastoral Applications
 Critics of oikobaptism delight to point out that such requirements would have excluded infants and small children, yet they fail to acknowledge other ways in which the Didache alters the simplicity of apostolic baptism.
 Hippolytus, and Burton Scott Easton. Apostolic Tradition. [Hamden, Conn.: Archon Books, 1962.,
 Allen Guelzo observes that “It is probably no accident that the first appearance in church history [of those who practice believers’ baptism only] occurs in the early 1500′s—in other words, they appear at exactly the same time the Renaissance was exalting the individual and creating a philosophy of man-centered individualism of which we are all heirs. This also explains the overwhelming popularity of Baptist churches in America, for what else is America, culturally speaking, but the land of the supreme individual—of the loner who goes off on his own, carves out his own private frontier empire, farms and protects it by his own hand, and makes, ‘Mind your own business’ his unofficial creed? Do we wonder, with this being so much a part of our natural culture, that the Baptist, with his parallel stress on individualism in spiritual things should bulk so large on our horizon?” Quoted in Booth, p. 125, n.6
 Ultimately, one’s view of baptism is determined by one’s hermeneutics (way of reading and interpreting the Bible). A “NT-Only” hermeneutic is more likely to yield a credo-baptist only view. A tota scriptura (OT and NT) hermeneutic is more likely to yield an oikobaptist view.
 The oikos formula is based on a diachronic reading of scripture whereas the credo-only formula is based on a synchronic (even anachronistic) reading of scripture.
 For more on this see http://www.catholic.com/tracts/early-teachings-on-infant-baptism
 This is not simply a Post-Reformation phenomenon. The church at Corinth fractured into “baptistic” sects in the times of the apostles (1 Cor 1:10-16).