The current form of the Byzantine rite is the result of the development of its liturgical books which have heterogonous origins (e.g., Constantinopolitan cathedral liturgical practice, Constantinopolitan monastic liturgical practice, the Palestinian monastic liturgical practice, and Jerusalemite cathedral liturgical practice). The Byzantine rite is thus an amalgam of different liturgical practices.
The most notably example is how the Euchologion, which originally belongs to the cathedral rite of Constantinople, has been combined with the Horologion, which originally belongs to the Palestinian monastic rite.
This is, for example, the reason why there are silent priestly prayers in Vespers and Matins since these prayers are remnants of the cathedral rite which did not really fit into the Palestinian monastic liturgical practice so they were bunched together to be read silently by the priest at the beginning of the service.
The liturgical books of the Byzantine rite became standardized through the invention of the printing press and the mass production of printed liturgical books.
The printing of Greek liturgical books was originally a private commercial enterprise in which Greek printers based in Venice produced the editiones principes in the early 16th century.
These printed editions which produced the standardized liturgical texts of the Byzantine rite were based on an arbitrary selection of manuscripts and often also included arbitrary editorial emendations.
From the 17th century onwards the Roman Catholic Church also began to print Byzantine liturgical books intended for Italo-Byzantine parishes and Uniates. The Roman editions were often superior from a philological perspective but also contained some unfortunate confessionally motived emendations intended to bring Byzantine liturgical practice more into line with post-Tridentine Catholicism.
It was first toward the end of the 19th century that official Greek editions of liturgical books began to be published by the Ecumenical Patriarchate. Unfortunately, these also reflect to a certain degree polemically or pastorally motivated editorial changes which deviate from the Byzantine manuscript tradition(s).
It was first in the 20th century that Greek scholars began to produce editions of liturgical books based on textual criticism and sound liturgical scholarship. A pioneer was Prof. Panayotis Trembelas (1886-1977) who edited the three liturgies and the Mikron Euchologion.
The most productive modern editor of liturgical books was Protopresbyter Constantine Papayannis (1929-2014), a collaborator of the prominent liturgical scholar Prof. John Fountoulis (1929-2007).
Papayannis worked as the main editor of the revised liturgical books published by Apostoliki Diakonia, the publishing house of the Church of Greece. His last contribution to the revision of the printed liturgical books was a posthumous edition of the Triodion. He also prepared editions published by other publishers, for example, an edition of the Horologion and a two-volume Anthologion.
However, the production of revised liturgical books based on textual criticism and liturgical scholarship in Greece does not seem to have come to end with the death of Papayannis in 2014. In the same year Dr Dionysios Anatolikiotis published a revised edition of the Euchologion to Mega based on textual criticism and scholarly principles. (One can also note that the Hellenic Bible Society published a Prophetologion in 2008.)
The following are the revised and critical editions of Greek liturgical books which to my knowledge are now in print:
P. Trembelas, ed., ΑΙ ΤΡΕΙΣ ΛΕΙΤΟΥΡΓΙΑΙ.
P. Trembelas, ed., ΜΙΚΡΟΝ ΕΥΧΟΛΟΓΙΟΝ, Τ. Α΄.
P. Trembelas, ed., ΜΙΚΡΟΝ ΕΥΧΟΛΟΓΙΟΝ, Τ. Β΄.
C. Papayannis, ed., ΩΡΟΛΟΓΙΟΝ ΤΟ ΜΕΓΑ.
C. Papayannis, ed., ΑΝΘΟΛΟΓΙΟΝ, Τ. Α΄.
C. Papayannis, ed., ΑΝΘΟΛΟΓΙΟΝ, Τ. Β΄.
C. Papayannis, ed., ΕΓΚΟΛΠΙΟΝ ΤΟΥ ΑΝΑΓΝΩΣΤΟΥ ΚΑΙ ΨΑΛΤΟΥ.
C. Papayannis, ed., ΙΕΡΑΤΙΚΟΝ.
C. Papayannis, ed., Η ΑΓΙΑ ΚΑΙ ΜΕΓΑΛΗ ΕΒΔΟΜΑΣ.
C. Papayannis, ed., ΤΡΙΩΔΙΟΝ.
C. Papayannis, ΣΥΣΤΗΜΑ ΤΥΠΙΚΟΥ.
D. Anatolikiotis, ed., ΕΥΧΟΛΟΓΙΟΝ ΤΟ ΜΕΓΑ.
Incidentally one can also note that Eastern Christian Publications are reprinting the four-volume Roman edition of the Greek Anthologion: vol. 1, vol. 2, vol. 3, vol. 4.
Finally, one can note that Archimandrite Nikodemos Skrettas has recently published a critical edition of the Typikon of St. Sabbas which can be ordered here.
Selected literature
C. Calivas, Essays in Theology and Liturgy, vol. 3: Aspects of Orthodox Worship, 2003.
J. Chupungco, ed., Handbook for Liturgical Studies, 5 vols., 1997-2000.
J. Getcha, The Typicon Decoded, 2012.
P. Meyendorff, Russia, Ritual, and Reform, 1991.
T. Pott, Byzantine Liturgical Reform, 2010.
F. Taft, The Byzantine Rite, 1992.
David Heith-Stade's blog 