A string of political outsiders are challenging in the kind of election which saw Hartlepool vote in the town's football club mascot as mayor.
Stoke South MP George Stevenson is trying to become the first sitting MP to become mayor but faces opposition from the other main parties, the British National Party and a range of independents.
Bedford, Hackney and Mansfield are the other areas electing the new-style mayors, having already voted in a referendum to create the role.
Key battles
In Hackney, east London, left-wing journalist Paul Foot is standing for the Socialist Alliance, but the council's Labour leader Jules Pipe is seen as the frontrunner there.
Mansfield Council's deputy leader, Lorna Carter, is Labour's candidate in the town, facing four other contenders.
Those include newsagent Tony Eggington, who played a major part in the referendum over whether to move to the new system, and candidates from the Conservatives, Lib Dems and Greens.
In Bedford, Frank Branston, of the Bedford Independent Party and founder of the Bedfordshire on Sunday newspaper, has been tipped as favourite by a town bookmaker.
But the three main parties, the Greens and three Independents are also contesting the seat.
Voting rules
Hackney is holding a postal ballot, which closes at 1800 BST (1700 GMT), while the other polls end at 2100 BST.
Voters can put their first and second preferences - if no candidate has more than half the votes, then the top two go forward to another count where the second choices are redistributed.
The full list of candidates for the elections is:
Bedford: Charles Rose (Conservative), Apu Bagchi (Labour), Christine McHugh (Liberal Democrat), Mark Powell (Green), Frank Branston, (Better Bedford Independent Party), Ian Clifton (Ind), Tom Foster (Ind), Gurminder Singh Dosanjh (Ind).
Hackney: Andy Boff (Con), Jules Pipe (Lab), Ian Sharer (Lib Dem), Crispin Truman (Green), Bruce Spenser (Hackney First), Errol Carr (Ind), Terry Edwards (Ind), Paul Foot (Soc All).
Mansfield: Kate Allsop (C), Lorna Carter (Lab), Phillip Smith (Lib Dem), Michael Comerford (Green), Tony Eggington (Ind).
Stoke-on-Trent: Roger Ibbs (C), George Stevenson (Lab), Fred Morrow (Lib Dem), Adrian Knapper (Adrian Knapper Independent Party), Steven Batkin (British National Party), David Chatton (Ind), Patricia Whitehouse (Ind), Graham Wilkes (Ind), Mike Wolfe (Mayor4Stoke Party), Paul Breeze (no description), Harry Chesters (no description), Geoffrey Snow (no description).