73 candidates are standing - 13 for each of the Conservative, Labour and Liberal Democrat parties, 12 for the Green Party, nine for UKIP, and eight for the Trade Unionists and Socialists Against Cuts.
There are also three candidates standing for the An Independence From Europe party one from the BNP and one from the Unity party.
Voting's also taking place for the European parliament elections.
Polling stations close at 10pm.
Exeter care agency rated 'inadequate' and in special measures
Bosses at Horizon Care insist change
Raw sewage spews into Plymouth suburb estate and woods
Concerns raised for public health and wildlife in Woolwell
Councillor stands under trees to stop chainsaw massacre
Emergency preservation order now in place
Three years jail for charity box thief
And he can't eat in McDonald's for eight years
Spat over whether 'inadequate' children's services are as bad as MP suggests
Exeter's Steve Race believes they are in 'last chance saloon;
Totnes market not opening in Christmas week
Most traders don't want to do it
