The LDS Church officially adopted Scouting as its youth program and has been a big part of the program ever since. The Church currently has the most youth registered out of all organized religions. However, the Church sponsors what are called "Non-Traditional Units," which means that we take part in the Scouting program, but with a few changes.
Why are there changes? Some have to do with Church policy, but usually it's because of some reasoning that brings the Scouting program a little more in line with the programs and precepts of the Church.
The first change is that the Church doesn't participate in the Tiger Cub program. The Tiger Cub program was introduced in 1982 and was made for 7-year-olds and their parents. It was a stand-alone program, and the Tigers weren't officially part of the Cub Scout Pack. However, that has since changed; in 2002 the Tiger Cub den was officially welcomed into the pack and Tiger Cubs got to wear the same dark blue uniform as other Cub Scouts. The Tiger Cub badge now occupies the spot that the Webelos badge did before, and a new oval shaped Webelos badge was introduced. Despite these changes, the LDS Church continues to sponsor Scouts only from the age of 8 through the 18th birthday.
Webelos and 11 Year Old Scouts
Webelos is a transitional program from Cub to Boy Scouts. Traditional Units often have a 18 to 24 month program for Webelos, which allows them to adjust to doing more with their Den and on their own. Usually when a boy earns his Arrow of Light award he is automatically promoted to the local Boy Scout Unit because he has learned all he can from the Webelos Program. The LDS Church sponsors 12 month Webelos units, and then a separate 11 Year Old Scout program (formerly called Blazer Scouts) when they turn 11.
Another thing that's a little different is that often, traditional units begin with the school year, and boys move from one den to the next at the end of the summer, rather than with their next birthday. This allows for bigger "graduation" ceremonies as whole groups of boys move onto the next den rather than one at a time.
Finances and Funds
In traditional units (which can be sponsored by a religious group or community organization like the Elk's Lodge, Rotary Club, Lion's Club, a local fire station, a school, etc.) the money to run the Unit comes from fundraisers and from dues paid by the Scout's family. In the LDS Church we tend to not have those because we use Church funds from Tithing to pay for such things.
As with all callings in the Church, Adult Leaders are called to their positions and given the choice to accept it. In Traditional Units leaders volunteer much like parents would with a PTA program.
The LDS Church automatically registers boys into Scouting from the age of 8 to 18, while other units have to have recruitment drives to find new boys to participate in the programs.
Like all religious groups that sponsor Scouting Units, the LDS Church has special religious Scouting awards. For Cub Scouts it is called the Faith in God Award and for Boy Scouts and Adult Leaders it is called the On My Honor Award. Often other religious units will have separate religious awards for each phase in scouting. This Wikipedia page has example of the different awards for different religions, with a chart showing what they look like here. More info can be found by following links from the Links page.