A grinding machine comprises two rotary tool spindles (4, 6), each able to carry at least twogrinding wheels (20, 22, 24), and a transfer mechanism (40, 64) operable to transfer a grinding wheel (22) mounted on one of the tool spindles onto the other tool spindle. Methods of operating such a machine, methods of grinding using such a machine, and a transferable grinding wheel (22) for use in such a machine are also disclosed.