Thompson has had a long and successful career in Wisconsin politics, but has not been on a ballot since 1998. He was first elected to the state Assembly in 1966, eventually becoming the Republican minority leader. He was elected governor in 1986, then re-elected in 1990, 1994 and 1998, before joining President George W. Bush's cabinet in 2001. He left the cabinet after the 2004 election, and briefly sought the Republican nomination for president in 2007, only to withdraw after a poor showing in the Ames Straw Poll.
Thompson was long courted by the GOP to run for Senate in various cycles, but never made the jump -- he came very close in 2010, but ultimately backed away.
Also, Thompson has been strongly opposed by the right-wing Club For Growth, which has released poll data suggesting that the relatively moderate Thompson could be vulnerable to a primary challenge from the right -- and have hinted that they could support such a challenger.