Canon 1D X has a Canon EF lens mount and currently there are 244 native lenses available for this mount.
Canon 1D X doesn't have a sensor based image stabilization system but 59 of these lenses already comes with optical image stabilization.
Since Canon 1D X has a Full frame sensor, it has a focal length multiplier of 1x so lenses will provide their original focal length on 1D X.
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Canon 1D X Lenses with Image Stabilization
Canon 1D X Lenses with Weather Sealings