This paper provides a comprehensive overview on the utilization of curved graded multilayer coatings as focusing elements for hard X-rays. It concentrates on the Kirkpatrick-Baez (KB) focusing setup that has been developed at 3rd generation synchrotron sources worldwide. The optical performance of these devices is evaluated applying analytical and numerical approaches. The essential role of the multilayer coating and its meridional d-spacing gradient are discussed as well as important technological issues. Experimental data and examples of operational KB focusing devices and applications complement the work.