Daniel Patte presents four ways of looking at the SM as delineations of discipleship.

A. Ethical (Deontological. also "Historical").  Strecker and Kingsbury uses redaction-critical and literary-critical methods.
The SM is a Law that determines the boundaries of the Christian community. The SM expresses the reality of Mattthew's time in terms of Jesus' unique time with his original disciples. The SM is an absolute expression of God's eternal will by God's unique Son. It is a law (but not a legalistic one) that disciples need to perform, and it is urgent that they do so because the coming of the Kingdom of God is imminent.
Discipleship is the implementation of God's eternal will as revealed by Jesus. It is presented as a set of universal principles that constitute a code of behavior for the church and its members.

B. Narrative.  Edwards uses plot analysis.
The SM is a call to discipleship.  The SM contributes to transforming its hearers into disciples who are fully ready to carry out their mission.  (Matthew is the story of how the lowly servant of all becomes exalted Lord of all, and how fishers become novice disciples and finally full-fledged disciples, equipped to carry out their mission to fish for people).
Discipleship is seeking to continue Jesus' ministry — by performing good works that other can discern as expressions of God's goodness and that can encourage them toward discipleship.

C. Figurative.  Luz, Davies, and Allison focus on taking the Lord's Prayer as central to the SM.
The SM specifies what discipleship involves in view of the fact that the disciples live between two horizons:  the present (in which God's love as a caring Father is manifest) and the future (the ethical demands of the coming Kingdom of God).
Discipleship is a faith venture in intuitive ethical practice.  Jesus is the primary model whom disciples are to imitate.

D. Thematic.  Patte focuses on taking the "sound eye" as the controlling theme in the SM.
The SM focuses on moral discernment, which distinguishes faithful discipleship. Being a faithful disciple means being totally focused on the manifestations of God's goodness, the good works of people, and the hidden good in righteous people.  The person who has such vision knows what direction to go in — imitating God and anyone else who performs good works.
Discipleship is a faith venture in which disciples seek by faith to discover what they must do.

This is the culmination of Betz' decades of study of the Sermon on the Mount. It also includes commentary on the Sermon on the Plain. It is a large book.

“A man comes forth in Israel to make today’s prophetic vision tomorrow’s agenda; one for whom the teachings of Mount Sinai do not suffice because he wished to penetrate beyond to the original divine intent; one who, despite war and tyranny, dares to pursue the biblical love of neighbor to its ultimate consequence in order to brand all our souls with an ideal of human possibility that no longer allows us to be content with the threadbare, run-of-the-mill persons we are but need not be” (7-8).

“What are all the imperatives of the Instruction on the Mount if not a concerted call to absolute fulfillment of the Torah in its original meaning, the concrete teaching of the all-encompassing love of God and love of neighbor?” (37).

A significant part of this book is Bonhoeffer's popular interpretation of the Sermon on the Mount.

This is a recent translation of Bonhoeffer's Nachfolge. This edition contains relatively extensive comments in footnotes. An earlier, popular translation is entitled The Cost of Discipleship.

This is the first volume in the series, Ancient Christian Commentary on Scripture. It is a modern "catena," a collection of noteworthy comments on verses in Matthew by church writers from the first century through the eighth. Each section is introduced by a summary, and then you see English translations of the comments from a fair variety of church writers.

An impressive commentary on the Gospel of Matthew, translated into English for the Hermeneia series.  This commentary discusses the meaning of each section with reference to Jesus, with reference to Matthew's community, and with reference to its influence.  Volume 1 contains the Sermon on the Mount.

This is a survey of some major Christian interpreters of the Sermon on the Mount, including John Chrysostom, Augustine, Hugh of St. Victor, Dante and Chaucer, Martin Luther, John Calvin, John Wesley, C. H. Spurgeon, Dietrich Bonhoeffer, John Howard Yoder, John Paul II, Leonardo Boff, and John R. W. Stott.