There are 22 county councils in Wales (also known as unitary authorities). There are 700 town and community councils, for which voting will take place on the same day.
POSSIBLE ISSUES
Council tax - Great unease in many parts. Is there an alternative, and how does it compare to other taxes?
Golden goodbyes - Who's left? Are they still a bunch of ageing white men?
People's parties - a lot of independent groupings setting up to challenge the main parties.
KEY COUNCIL BATTLES
Rhondda Cynon Taf - This is the big target council for Labour and likely to be the bitterest fight. For Welsh Labour, Plaid Cymru running the council in its heartland is very painful. Plaid will play up that it has won many UK-wide awards for its running of the authority.
Caerphilly - The other big Labour target, trying to win it back from Plaid Cymru.
Cardiff - Wales' most controversial council leader Russell Goodway faces a strong challenge from the Liberal Democrats.
Ceredigion - Following the overwhelming rejection in the 20 May referendum of proposals for a directly-elected mayor, the Independents try to maintain their grip on power with Plaid Cymru and the Liberal Democrats as main challengers.
Wrexham - John Marek's new party Forward Wales tries to make an impact.
Flintshire - A much-criticised Labour council faces voters.
Ynys Mon - Will the much-troubled and divided authority face more political turmoil?
Carmarthenshire - No single party has managed to dominate in recent years. What will happen this time?
Swansea - The city has lost its leisure centre - but do the swimmers care enough to vote?
Vale of Glamorgan - The Conservatives' only council and one they need to consolidate.
Monmouthshire - The Conservatives will be fighting to take Monmouthshire from Labour in what could be an extremely close contest.