Since his papacy began in 2013, Pope Francis has established himself as a people's pope. He is popular around the world and has a reputation as a reformer, able to reinvigorate the Catholic Church for the modern age.

But how successful have his reforms been? And are his stances on contentious issues such as divorce and homosexuality too progressive for some of the followers of the Church he leads?

For Austen Ivereigh, author of The Great Reformer: Francis and the Making of a Radical Pope, criticisms of Pope Francis for being too liberal are misplaced.

"[T]he shift that Pope Francis has introduced, and I agree it is a significant shift, is not an adaptation to modernity," says Ivereigh. "It is the recovery of a deeper tradition within the Church, which, sadly, some people who have a particular idea of what the church and the pope should be, simply don't recognise."

"When Francis was elected, I celebrated that election," says Matthew Schmitz, literary editor of religious magazine First Things. "The reason I've come to change my mind is that I've seen that Francis is building his programme of supposed reform at the expense not only of the Church but also at the expense of its most vulnerable members."

In this week's Arena, Catholic writers and analysts Austen Ivereigh and Matthew Schmitz debate Pope Francis' reforms to the Catholic Church.