A grinding media handling system for a vertical grinding mill comprises: a reservoir; a pump, such as a sump pump or a horizontal pump, for pumping water and/or a slurry of material to be ground from the reservoir via an inlet in an upper section of the vertical grinding mill into a grinding chamber of the mill; means for adding grinding media to the water and/or slurry upstream and/or downstream of the pump; and means for discharging slurry and grinding media from a lower section of the vertical mill.