Tensions with other faiths
There has been friction between the Roman Catholic Church and Muslims, Jews and Anglicans, and while Pope Benedict has tried to build some bridges, relations have not always improved.
Islam in particular poses a challenge since it is on the rise in Africa and Asia where Roman Catholicism has a large and growing base. Improving relations with Muslims proved difficult for Pope Benedict, who enraged many in 2006 by quoting from a 14th-century Byzantine emperor who labelled Mohammed "evil and inhuman."
The new pope will have to learn how to improve relations with Islam without denouncing the religion, antagonizing Jews or raising concerns in the West about being soft on violence by Islamic groups.
The church's relationship with Jews has also been difficult over the years and it was not helped by Pope Benedict putting Pope Pius XII on the track for sainthood even though the Second-World-War-era pontiff he has been criticized for not having done enough to prevent the Holocaust. And Anglicans had trouble with Pope Benedict after he encouraged those disaffected with the Church of England to become Roman Catholics.
The church's relationships with Jews and Anglicans have gotten better lately, but keeping them on track won't be easy.
The church faces lawsuits, not to mention seething anger, from thousands of people in North America and Europe who were victims of abuse by priests. The new pope will have to be attuned to pressures from Western countries, including Canada, that have prosecuted priests accused of sexual assault.
Many saw Pope Benedict as a major obstacle in the issue, although he has apologized and spoken of the church's shame. The incoming pope will have to find a way to resolve the legal action, which could be costly, and to be more open. He will also have to overcome right-wing elements within the Vatican that have taken a hard line and refused to negotiate or admit wrongdoing by priests.
Contraception and abortion
Few issues divide the church as much or leave it as vulnerable to accusations of being out of touch. Here again the new pope will have to carefully weigh church doctrine with health concerns in places like Africa where condoms are considered a life-saving protection from AIDS.
Pope Benedict sparked outrage by suggesting during his first trip to Africa that distributing condoms "aggravates the problems." He later modified his position and said the use of condoms was acceptable "in certain cases."
On abortion, the challenge is Western attitudes: Consider the outrage sparked by Canadian Cardinal Mark Ouelllet's comments in 2010 that abortion is a "moral crime" and never acceptable, even in cases of sexual assault.
Same-sex marriage and homosexuals
This issue has left Catholics in much the same place as Anglicans – being seen as out of touch in the West and winning wide support in Africa.
More countries in Europe are moving toward legalization of same-sex marriage despite fierce opposition from the Vatican and comments from Pope Benedict that gay marriage destroys "the essence of the human creature."
With the church losing members in Europe and North America, can a new pope address these issues without eroding the base further and without upsetting the church in Africa where Catholicism is growing?
Perhaps the greatest challenge for the new pope will be the relevance and use of Vatican authority in such a changing and complex world. Do directives from the pope on various issues, such as abortion, contraception and other social issues, help or hinder responses to those issues?
Pope Benedict believed strongly in the importance of laying down fundamental truths and teachings. But with deep divisions between developed and developing countries on so many fronts, the new pope will have to decide whether to use papal pronouncements to tackle these issues.