Update 2: Philip Hammond has just been confirmed as the new Defence Secretary. Justine Greening, the economic secretary to the Treasury, replaces him at Transport. As expected, Cameron avoided a full-scale reshuffle, something that he will want to perform at a time of his choosing.
Update: Cameron has just made a short statement in which he said that he would announce Fox's replacement "very shortly". This suggests that a major reshuffle is unlikely. One easy option would be to move Hammond to Defence and to appoint his deputy, Theresa Villiers, as the new Transport Secretary.
Following Liam Fox's resignation, attention has swiftly turned to the question of his successor. Philip Hammond, the Transport Secretary, widely seen as a competent technocrat, is the favourite to replace Fox. Other names in the frame include Owen Paterson, the Northern Ireland Secretary, and Andrew Mitchell, a former soldier who served in the 1st Royal Tank Regiment. Fox's replacement is likely to come from within the cabinet but another option would be to bring back Malcolm Rifkind, who served as Defence Secretary from 1992-1995, as a straight swap for Fox.
Another question being debated in Westminster is whether Cameron will use this opportunity to carry out a full reshuffle, something that would allow him to move the increasingly troublesome Ken Clarke. His key challenge is to maintain the political balance of the cabinet and to keep the Conservative right - which lionised Fox - on side.