A third of all 69 seats are up for election - one seat in all of Kirklees’ 23 wards.
Kirklees Council is currently in no overall control with Labour (33 seats), Conservatives (19 seats), Liberal Democrats (nine seats), Greens (three seats), Holme Valley North Independents (three seats) and other Independents (two seats).
Of the seats up for election this year, Labour hold 11, Conservatives six, Lib Dems four, Holme Valley North Independents one and Greens one.
Polling stations around the district will be open until 10pm today (Thursday).
The count will take place at Cathedral House in Huddersfield tomorrow (Friday), with results expected to be announced during the afternoon.