The inquiry is being coordinated by the National Association of Local Councils, which represents the interests of England's 8,500 town and parish councils.
It is asking key stakeholders in local government and beyond for their analysis, insight and advice on where localism needs to go next.
Findings will be made available to the government, the All-Party Parliamentary Group on Local Democracy and local councils themselves.
The inquiry is being run in conjunction with the All Party Parliamentary Group on local democracy, which is chaired by Rory Stewart, MP for Penrith and the Borders.
A booklet of thought-provoking articles by key thinkers across the political spectrum accompanies the inquiry, said NALC head of policy Justin Griggs.
"We want to get people thinking about the future of local councils and generating ideas about how the current policy, legislative and financial frameworks can be improved.
"We're interested in finding out what support is needed to really unlock the capacity and potential of local councils – including everyone working in and around them – and in exploring what can be done to enhance their delivery capability and productivity.
"More than anything we hope through the inquiry to come up with radical new ideas to help hyper local democracy truly flourish into the future."
Mr Griggs said he hoped to hear from everyone with an interest and passion for local democracy and community action – whether they were involved locally or nationally.
Stakeholders are encouraged to share their ideas – as well as rating and commenting on the thoughts of others – through a dedicated website at www.whatnextforlocalism.org.