Millions of people in England and Wales are eligible to vote after polling stations opened at 07:00 on Thursday.
There are elections in 107 local authorities across England, as well as 11 mayoral races.
A by-election will elect a new Blackpool South MP, following the resignation of former Conservative Scott Benton.
And voters across England and Wales will elect 37 police and crime commissioners (PCCs).
There are no elections in Scotland or Northern Ireland.
Counting will begin after the polls close, at 22:00 on Thursday, with the first results expected after midnight on Friday, 3 May.
Results will continue to arrive throughout Friday and over the weekend, with the last due on Sunday afternoon.
Mayoral results – including those in Greater London, West Midlands and Greater Manchester – will be announced on Friday and Saturday.
London Assembly election declarations will also come through on Saturday.
And the winner of the Blackpool South by-election is expected to be announced early on Friday.
In-person voters will need to show one of the 22 accepted forms of identification, including passports and driving licences.
While polls are open, the BBC, like other broadcasters, is not allowed to report details of campaigning or election issues.
The BBC does not report on any of the election campaigns, on television, radio or bbc.co.uk, from 00:30 until 22:00 on polling day although it can report on political events and stories not directly related to the elections.
Source: BBC
