Did you know that The Church of Jesus Christ of Latter-day Saints Public Affairs department has a YouTube account? Many of the videos address basic doctrines, and some focus on current affairs. Following are some of the videos that are online.
Watch Elder Ballard addressing the question, “Are Mormons Christian?”
Elder Cook talks about the need to make a clear distinction between our Church, and the FLDS group that practices polygamy here.
And here’s one about the Church’s recent efforts to help in Myanmar.
There are many others, under the username LDSPublicAffairs