Why it could blow up: Tillerson has extensive business ties to Russia and, specifically, to President Vladimir Putin. The two worked together to seal energy and drilling deals in the face of U.S. sanctions against Russia, and Tillerson even accepted an award from Moscow. German newspaper Suddeutsche Zeitung reported that Tillerson also ran a U.S.-Russian oil firm in the Bahamas, a tax haven (and reminiscent of the offshoring Trump has said he wants to crack down on.)