Men and Women both compete in:
Freestyle skiing has been one of the fastest growing olympic events over the last few decades. After starting with just 2 events in 1992, the event has nearly doubled in size going from awarding 6 medals in Vancouver to 10 medals that will be awarded in Sochi. Moguls, Aerials and Ski Cross are the returning events with Half-pipe and Slopestyle being added for both Men's and Women's competition. Moguls requires athletes to navigate a course with mounds of snow and two jumps. Judges score competitors based on speed, ability to navigate moguls and the quality of jumps. Aerials takes the navigation aspect out of the equation and simply consists of two jumps where competitors are judged based on technique for takeoff, form and landing. Ski cross is a downhill race where competitors race in groups of four through a course of turns and obstacles. The Halfpipe should be familiar to American audiences that have seen the X Games as it has been a staple of that competition for years, both for snowboarders and skiers. Slopestyle is basically like Tricks Mode in 1080 Snowboarding for N64. Competitors perform tricks using various obstacles as they navigate their way down a slope and are scored based on the difficulty and quality of the tricks they perform.
As the countries that pioneered the X Games, it should be no surprise that the United States and Canada have cleaned house in Freestyle Ski events. Of the 24 Olympic Golds, 6 have been won by the US and 4 by Canada. On the whole, the US has won 14 Freestyle medals and Canada has won 9. The Chinese contingent are the sleepers in this event after winning 3 of the 6 medals in Aerials in Vancouver.
The US has dominated in the Moguls events, winning 10 of their 14 Freestyle medals there. Defending Gold medalist Hannah Kearney is one of the best freestyle skiers in the world, and won 11 of 13 World Cup events in 2012. The US figures to be competitive in Moguls, Skicross, Halfpipe and Slopestyle where the X Games athletes will have a leg up on the competition.
Don't bet against the US and Canada when it's something similar to the X Games. Norwegians are always good when they have skis on their feet and the Chinese will be competitive in the Aerials competitions. Austrialians have won Freestyle medals in each of the last 3 Olympics.