Ladbrokes' data wonks have been busy calculating odds and this is what we have so far.
They have Chris Graying as a strong favourite home secretary, offering odds of 2/1 on the appointment.
Grayling, a former Leave campaigner, is running May's campaign. He said today that she will choose the best people available for her cabinet and appoint a "strong, balanced, sensible team", while being mindful of the need to unite the party.
Both Osborne and Johnson had been favourites to take the Tory throne, but the former London mayor pulled out at the last minute while Osborne's chances appeared to be scuppered after the Leave vote won.
The bookmaker thinks he'll switch places with current foreign secretary Philip Hammond, who they put on 1/2 favourite for role of chancellor.
Hammond said today that negotiations could take up to four years to negotiate an exit from the EU.