Today, Pope Francis is meeting with various Bishops to discuss marriage and the family. The buildup to this has been pretty messy in Catholic circles, as everyone is gathering around their respective flags and brutally attacking everyone who disagrees.
The most popular fight is over divorce. The Catholic Church does not allow for divorce, because Jesus Christ doesn't allow for divorce. Jesus gets asked about marriage and divorce several times in the Bible, and he always responds that marriage is permanent, so divorce is impossible. Despite this, Catholics get divorced at about the same rate as non-Catholics. They just go to the government to get a divorce.
So the big debate is "what should the Church do about divorced and/or remarried people?". It's especially tricky dealing with remarried people, because oftentimes, they're married to Person A in the eyes of the Church, while they're married to Person B in the eyes of the government. So technically, they're married to two people, which is more or less asking for adultery to occur.
Personally, I'm hoping that they will decide to let priests get married. They used to have married priests, and I think that's one tradition that should be revived. If Pope Francis does reinstate that rule--which is a long shot--I am not sure that the United States Bishops will be able to get a two-thirds majority vote to approve it. We could very well have a situation where priests can get married, but not in the United States.
[Edit: I'm hoping priests can get married, because I'm engaged to get married! And I was enrolled in priest school for three years. I guess you could say I got the best of both worlds!]
Another issue people are talking about is "cohabitation". The Church is against two people living with each other, before they get married. (That would include me!). Some people are arguing that this position is a holdover from the times when everyone had to live with their parents before marriage, and now that society has changed, the Church's position on cohabitation should change, too.
Gay marriage may or may not get mentioned. Pope Francis seems more interested in the topic than the Bishops are, but that could just be because the media goes into a reporting frenzy whenever the Pope mentions gay people, while the media usually ignores Bishops when they mention gay people.