The cyclin-dependent kinases 4 and 6 (Cdk4/6) that control the G1 phase of the cell cycle and their inhibitor, the p16INK4a tumour suppressor, have a central role in cell proliferation and in tumorigenesis. The structures of Cdk6 bound to p16INK4a and to the related p19INK4d reveal that the INK4 inhibitors bind next to the ATP-binding site of the catalytic cleft, opposite where the activating cyclin subunit binds. They prevent cyclin binding indirectly by causing structural changes that propagate to the cyclin-binding site. The INK4 inhibitors also distort the kinase catalytic cleft and interfere with ATP binding, which explains how they can inhibit the preassembled Cdk4/6-cyclin D complexes as well. Tumour-derived mutations in INK4a and Cdk4 map to interface contacts, solidifying the role of CDK binding and inhibition in the tumour suppressor activity of p16INK4a.