The Orthodox Church follows a different calendar to those in the West, with the birth of Jesus falling on the 7 January instead of 25 December.
The chief festivities took place last night, with Mass celebrated in various cities around the world.
The Russian President Vladimir Putin and Prime Minister Dmitry Medvedev attended separate church gatherings last night.
The Egyptian President Abdel Fattah el-Sisi has used a mass in Cairo to promise to rebuild every Egyptian church damaged or destroyed in sectarian violence within a year.
Bishop Angaelos, of the Coptic Orthodox Church in the UK, told Premier's Inspirational Breakfast: "We still work on the Julian calendar... But for us Christmas is exactly the same. It's the celebration of the nativity of Christ, the incarnation.
"It meant I was able to join the Bishop of London and the Dean of St Paul's [Cathedral] at the Midnight Mass on Christmas Eve, and the Archbishop of Canterbury in Canterbury on Christmas Day.
"We had the equivalent of a Midnight Mass yesterday, and today will end up being a family day for most people."
Listen to Bishop Angaelos speaking to Premier's John Pantry on Inspirational Breakfast: