The renewed increase in atmospheric methane (CH₄) concentrations since 2007, culminating in record growth rates in 2021, poses a critical challenge to achieving global climate targets. The TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor satellite provides unprecedented daily global observations of CH₄ at a spatial resolution (7 × 7 km², improved to 5.5 × 7 km² since August 2019), enabling substantial advances in space-based CH₄ monitoring and emission quantification. Here, we synthesize and categorize 133 published studies spanning global, regional and local scales and covering both anthropogenic and natural CH₄ sources. Collectively, these studies demonstrate TROPOMI's capability to quantify emissions across diverse spatiotemporal scales, as well as its synergy with other satellite instruments for detecting and attributing facility-level sources, such as fossil fuel infrastructure and landfills. However, emission estimates remain challenged by uncertainties in column-averaged CH4 (XCH₄) retrievals related to surface albedo effects and persistent cloud cover, particularly in tropical and high-latitude regions. These limitations can be mitigated through improved retrieval algorithms, refined quality filtering, multisatellite fusion, and integration with ground-based observations and airborne campaigns. Furthermore, we assess the suitability of different quantification approaches for specific source types, such as Gaussian plume models for large isolated emitters and inverse modeling for spatially diffuse emissions. Finally, we outline key methodological priorities and opportunities in the context of the recent MetOp-SG-A satellite, which will complement TROPOMI with a morning overpass. By consolidating current applications of TROPOMI XCH₄ observations, this review provides guidance for enhancing space-based methane monitoring and supports targeted mitigation strategies aligned with achieving Sustainable Development Goal 13.