Old Calendarists

An Old Calendarist is any Eastern Orthodox Christian who uses the Julian calendar - also called the "Old Style Calendar", "Church Calendar" or "Old Calendar" - and whose church body is not in communion with the Eastern Orthodox churches that use the Revised Julian calendar which aligns with the Gregorian calendar.
Background.
Most churches which use the Old (Julian) Calendar are "not" Old Calendarists: they remain in communion with the Eastern Orthodox Churches that use the New Calendar (the Revised Julian calendar). Thus, to be "Old Calendarist" or "Old Calendar" is not the same thing as being "on the Old Calendar". The Russian Orthodox Church, for instance, is not Old Calendarist (or Old Calendar), but it is on the Old Calendar. There are a great many Eastern Orthodox Christians who are (or who belong to Churches that are) "on the Old Calendar", but far fewer in number are the Eastern Orthodox Christians who are "Old Calendar" or "Old Calendarist." 
Schism.
The Revised Julian calendar was first used as a civil calendar in Greece and was later adopted by some Eastern Orthodox churches. A minority of Eastern Orthodox Christians regarded this as a surrender of the Eastern Orthodox Church to the Pope and continued following the old, Julian calendar. Some of these also broke communion with those who had adopted the new calendar, thus creating their own church, or denomination. This schism is the beginning of the Old Calendar Churches which suspended full communion or concelebration with other Eastern Orthodox churches ("New Calendarists") over the adoption by the latter of the Revised Julian calendar (called "New Calendar," although some churches did not specify the details of which "New calendar" they were adopting).
Those Orthodox Churches which remain in full communion with the New Calendarists and yet continue to use the Julian calendar include the Eastern Orthodox Patriarchate of Jerusalem, the Russian Orthodox Church, the Serbian Orthodox Church, and the Georgian Orthodox Church. (The Julian calendar is also used by the Russian Orthodox Church Outside of Russia which has reunited with the Russian Orthodox Church.) Mount Athos, subordinate to the Patriarchate of Constantinople, also follows the Julian calendar.