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Many direct attempts to measure the proper motions of Galactic satellite galaxies are either in progress or have recently been completed. In this review I will summarise and examine the current state of knowledge in this field and will also highlight several indirect methods that can be used as alternative estimators or constraints on the proper motions of satellite galaxies throughout the Local Group. A good example of this latter approach is provided by the Sagittarius dwarf galaxy, wheredoi:10.1017/s0074180900204439 fatcat:eukpo2w5dfbvdldvxh6mjpsy24