Cohen was first elected to the Minnesota Legislature in 1976. He served as a member of the Minnesota House of Representatives for District 63B and, after redistricting in 1982, for District 64B. He was elected senator for District 64 in 1986, gaining the lone Republican-held Senate seat within the Twin Cities.[2] He was reelected in the 1990, 1992, 1996, 2000, 2002, 2006, 2010, 2012, and 2016 elections.
Cohen was chair of the Senate Finance Committee from 2003 to 2011 and chair of the Senate State Government Finance Committee from 1997 to 2001.[1]
On November 3, 2009, President Barack Obama announced Cohen's appointment to the President's Committee on the Arts and Humanities. Cohen is considered by many to be the leading champion for the arts in the Minnesota Legislature. He led the campaign to include funding for the arts in the Clean Water, Land and Legacy constitutional amendment that Minnesota voters approved in 2008.[3]
In 2019, Erin Murphy announced that she would be running to unseat Cohen in the DFL primary.
On November 17, Cohen announced that he would not be running for re-election in 2020.[4]
