What is the significance of the Julian calendar for the Orthodox church? Why do many Orthodox churches continue to use the Julian calendar?
Today, many Orthodox churches use a Revised Julian Calendar, which largely corresponds to the Gregorian calendar used throughout the rest of Christendom, with the exception of the date of Easter.

The dating of Easter is seen by some, like Lewis J. Patsavos of the Greek Orthodox Archdiocese of America, as the primary reason that Orthodox churches originally rejected the Gregorian Calendar when it was presented in the 16th century:


  Despite the efforts of the emissaries of Pope Gregory to convince the Orthodox to accept the New (Gregorian) Calendar, the Orthodox Church rejected it. The main reason for its rejection was that the celebration of Easter would be altered: contrary to the injunctions of canon 7 of the Holy Apostles, the decree of the First Ecumenical Synod, and canon 1 of Ancyra, Easter would sometimes coincide with the Jewish Passover in the Gregorian calendar.


The aforementioned canon of the Apostolic Canons reads:


  If any bishop, presbyter, or deacon, shall celebrate the holy day of Easter before the vernal equinox, with the Jews, let him be deposed.


To avoid this issue, a Revised Julian Calendar was adopted by many Orthodox churches in the early 20th century.  Such churches follow the Western calendar except in the case of Easter, for which they maintain the original calculation.  Thus, the date of Easter for the vast majority of Eastern Orthodox churches continues to often be one or more weeks after the Western date.

For others, the root issue in the 16th century was not the date of Easter but rather papal authority.  John W. Morris writes:


  When first introduced, acceptance of the Gregorian Calendar implied the recognition of the authority of the Pope. (The Historic Church, 506)


But Morris recognizes that many continue to reject even the revised calendar, and attributes this to "rigidity" and "legalism" over "non-essentials such as the calendar." (508)  Timothy Ware describes the "Old Calendarists" more neutrally:


  The Old Calendarists see the change in the calendar as the first in a long series of innovations which, so they believe, have corrupted the mainstream Orthodox Churches in the twentieth century.  In their view, what is at stake is not just a technical mater of thirteen days, but the purity of the Orthodox faith. (The Orthodox Church)