Elections are being held in more than 150 councils, while mayoral elections will take place in Watford, Hackney, Newham, Lewisham and Tower Hamlets.
There are no local elections in Scotland, Wales and Northern Ireland but some 4,500 seats are being contested across England.
This year, new rules for voter ID are being piloted in Bromley, Gosport, Swindon, Watford and Woking which will see voters forced to prove their identity before voting.
Ministers say the controversial rules will safeguard votes but critics say it will put people off.
Polling stations opened at 7am and will close at 10pm, with the first results expected to come in after midnight.iPhone transfer software Do you need a polling card?
You can find details of your nearest polling station on the card sent to you by the council in the post.
You do not need to take the card with you in order to vote as staff will have your details already so just give them your name and address on arrival.
AFP/GettyLocal elections 2018 TODAY: Jeremy Corbyn and Theresa May
If you have lost your polling card, visit yourvotematters.co.uk and type in your