In Global Navigation Satellite Systems (GNSS), the on-board clocks are a key component from which timing and navigation signals are generated. This thesis reviews the performance of the first Passive Hydrogen Maser (PHM) launched by the Galileo system in 2008, and demonstrates how the new PHM can be consider as the best clock in space, pushing the physical clock error contribution below the noise floor of geodetic time transfer capabilities. Furthermore, overall GNSS clock peformance is reviewedThis work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.