With all the talk that China will use the Varyag to rule the western Pacific, I would like to explain why the Varyag will NOT be a SERIOUS threat to the U.S. military or the U.S.'s interests in the region.
First, the Chinese navy has no experience with carrier operations, specifically: operating cat and trap systems, landing aircraft on a moving surface, replenishing large ships while underway, and launching, arming, fueling, and repairing aircraft in heavy seas. On top of that all these shortcomings are aggravated during combat operations, as all activities will have to be done faster, at the same time with an increased degree of precision.
Second, the Varyag is of the Admiral Kuznetsov-class, and has a relatively small air wing of 26 fixed-wing aircraft (J-15, New AEW&C aircraft), and 24 helicopters (Ka-27), for a grand total of 50 aircraft. 50 aircraft is decent number for a second-tier military (Britain, France, Spain, etc...), but in a drawn out war with the U.S., 50 aircraft (of which less than half are fighters) will be nothing. Against 5+ American supercarriers, each carrying 100 aircraft, 50+ of which are fighters (not including aircraft from Japan, Guam, South Korea, and possibly the Philippines), 20 +/- fighters will be nothing.
Third, China has no escorts for the Varyag. One of the most important things needed to operate an aircraft carrier is destroyers for ASW (anti-submarine warfare) and air defense. You also need submarines to make sure no enemy submarines get close enough to take a shot at the Varyag or any of the escorts. China has both of these types of ships, but either in limited quantity or of lousy quality or both (China's nuclear submarines make enough underwater noise to make a U2 concert sound quiet). China does have diesel electric Kilo-class subs that are extremely quiet, but are too slow to escort a carrier task force. China also is beginning to build Type 052C destroyers which have a greater air defense capability than previous classes, and will probably form the backbone of Chinese carrier task forces.
Fourth, the Chinese will need a much better supply system to keep the Varyag at sea for extended periods of time. As of June 2011 the Chinese navy has a rather limited at-sea supply system, which is essential for operating an aircraft carrier(s).
While the Varyag is the only aircraft carrier the Chinese have, it will not pose a serious threat to the U.S.military. However, the Chinese military has expressed interest in building more carriers, but until the Chinese are able to field 3+ carriers with large air wings, the Varyag will not pose a serious threat.