According to the National Park Service,

Park rangers began search efforts on Sunday, April 17, 2011, after the Evgenia Buzulukova and Jonathan Wilson's vehicle was discovered at the Left Fork of North Creek Trailhead. The search continued into Monday, April 18 and was greatly expanded on Tuesday, April 19 when the couple were officially listed as missing. At that point there were 25 park rangers, park employees and volunteers involved in the search effort with support assistance including a helicopter, dog teams and multiple ground search teams.

Buzulukova and Wilson had a backcountry permit for a one day trip through Russell Gulch and the Left Fork of North Creek (The Subway) on Saturday, April 16. This area is located near the Kolob Terrace Road in the park approximately 15 miles north of Virgin, Utah. They eventually reached a point in The Subway where the very high and cold water conditions were such that they did not think it was safe to continue. They decided to wait at this spot for help from other hikers who may be in The Subway.