Millions of Orthodox Christians around the world are celebrating the birth of Jesus today.
Coptic Pope Tawadros II said in a message for the occasion that he wanted people to live lives of love and "do good" to others.
"Humanity is fulfilled when people live in love," he said.
"When a person acts, lives, offers this love, it becomes a way to achieve his or her humanity."
He added: "Christmas is a new beginning. Christmas is a new joy. Christmas is a new message for each person to begin a new year glorifying God."
In the UK, Archbishop Angaelos of London reminded people of the need to live with hope.
Speaking about the Orthodox Christmas with the Rev Kate Bottley on BBC Radio 2, he said: "Christmas is a time of giving and a time of joy, whether we're celebrating it on the 25th, the 6th or 7th.
"The Christian message is one of hope, and when you're reading the news and following your news feeds these days, there's so much hopelessness and so much sadness.
"And the best gift that we can give - that we've been given by God in the incarnation - is hope. So we give each other hope and joy."
Reflecting on societal divisions in the UK over Brexit, as well as conflict in the wider world, Archbishop Angaelos said it was important to work towards reconciliation.
"The more we can reconcile quickly and realise that we do co-exist, we must be together, we must share a space, and a life, and a vision, and a future, and work towards that reconciliation and common ground, the quicker we get over conflict and the more we can work towards building something positive.
"We've lost so much time in our nation here over Brexit - we've lost years," he said. "And at the end of the day we will have to find a solution ahead.
"But in other places like the Middle East and in other places where there is conflict, we must look forward, rather than constantly looking back with a sense of loss and a sense of hopelessness, to where we can go and what we can do, rather than what we can't."
The Archbishop of Canterbury said in a message to Orthodox Christians: "Christ, in his incarnation, gathers into one things earthly and heavenly.
"Wishing a blessed Christmas to our brothers and sisters in the Orthodox and Oriental Orthodox Churches today and tomorrow as you celebrate the birth of Jesus."
Pope Francis, in his message, said he wished Orthodox communities "the light and peace of Christ the Saviour".