Not all seats in England’s councils are been contested, South Yorkshire is voting for a regional mayor, while Bristol is holding a local referendum to decide whether the city council should continue to be led by a mayor.
In England, there are elections for 144 of 333 councils. That includes all the London boroughs, 33 out of 36 metropolitan boroughs, 60 of 181 district councils, and 21 out of 58 unitary authorities.
It is different in Wales and Scotland, where all local authorities are up for election.
In Northern Ireland, voters will choose 90 members of the devolved assembly. The Northern Ireland Assembly at Stormont is designed to make up a government in which power is shared between unionists, who favour remaining part of the UK, and nationalists, who support a united Ireland.
The elections take place throughout the day and polls closes at 10pm and results will be declared over the coming couple of days.
In England, Wales and Scotland, local representatives (known as councillors) are elected to represent their community and make decisions on delivering local services.
There are different types of councils which are responsible for particular services within their area.