Groundwater drought is a condition characterized by a significant decline in groundwater levels, resulting in reduced well yields or wells running dry. It commonly arises from prolonged and excessive groundwater pumping, which accelerates aquifer depletion and lowers the water table. This condition is often exacerbated by extended periods of drought and high evaporation, which limit natural recharge and further stress groundwater systems. Unlike other types of drought, groundwater drought is difficult to monitor due to limited or lack of direct observational data. A major barrier to understanding aquifer responses during extreme or prolonged drought is the scarcity (or lack) of reliable data on groundwater pumping. Furthermore, the reliance on meteorological-based drought indicators, which do not adequately capture sub-surface processes, limits our ability to assess the impacts of pumping on groundwater systems and the onset of groundwater drought. These challenges underscore the urgent need for integrated and more robust methods for groundwater drought assessment. This chapter examines opportunities and methods for monitoring and characterizing groundwater drought, emphasizing their relevance for sustainable water management, early warning systems, climate adaptation, and ecosystem protection. It highlights the role of satellite gravimetry missionsGravimetry missions such as the Gravity Recovery And Climate Experiment (GRACE) in enabling large-scale groundwater drought monitoring and characterization. While also addressing limitations associated with its coarse spatial resolution, this chapter articulates the potential of satellite geodetic-based drought indicators (e.g. GRACE, Global Navigation Satellite System-GNSS) for promoting groundwater drought and water resources assessment. The chapter also explores recent advances in statistical and machine learning-based downscaling techniques that enhance the spatial resolution of GRACE data for hydrological and groundwater drought assessment. Such capability enables the use of GRACE-derived groundwater product for local-scale assessment and decision-making on water resources. As further discussed in this chapter, there are opportunities to integrate radar data, GNSS-derived displacements, and terrestrial water storage changes observed by GRACE satellites within a multivariate framework to monitor groundwater storage losses and potentially characterize hydrological and groundwater drought.