Polling stations opened their doors at 07:00 BST and will close at 22:00.
Votes are being cast in council elections in Knowsley, Sefton, St Helens and Wirral. In Liverpool, voters will also elect a city mayor.
Voters across Merseyside will also be asked to choose a police and crime commissioner. In England, elections are taking place for more than 120 councils and the London Assembly.

11 August 2015 Last updated at 19:18 BST
Safid has travelled 5,000 miles from his home and is currently one of thousands of migrants living in a camp called the Jungle in Calais, France.
It's thought more than 600 child migrants arrived in the UK without their parents last month alone.
And Safid told Newsround reporter Martin Dougan that he will do whatever it takes to try and get to Britain soon.
Find out why child migrants want to come to the UK
Voting has begun in local elections across Merseyside.
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An 11-year-old migrant from Afghanistan has been speaking to Newsround about being separated from his father during a year long trip to try and reach the UK.