Two atmospheric inversions (one fine-resolved and one process-discriminating) and a process-based model for land surface exchanges are brought together to analyse the variations of methane emissions from 1990 to 2009. A focus is put on the role of natural wetlands and on the years 2000-2006, a period of stable atmospheric concentrations. From 1990 to 2000, the top-down and bottom-up visions agree on the time-phasing of global total and wetland emission anomalies. The process-discriminating inversion indicates that wetlands dominate the time-variability of methane emissions (90% of the total variability). The contribution of tropical wetlands to the anomalies is found to be large, especially during the post-Pinatubo years (global negative anomalies with minima between -41 and -19 Tg yr(-1) in 1992) and during the alternate 1997-1998 El-Nino/1998-1999 La-Nina (maximal anomalies in tropical regions between +16 and +22 Tg yr(-1) for the inversions and anomalies due to tropical wetlands between +12 and +17 Tg yr(-1) for the process-based model). Between 2000 and 2006, during the stagnation of methane concentrations in the atmosphere, the top-down and bottom-up approaches agree on the fact that South America is the main region contributing to anomalies in natural wetland emissions, but they disagree on the sign and magnitude of the flux trend in the Amazon basin. A negative trend (-3.9 +/- 1.3 Tg yr(-1)) is inferred by the process-discriminating inversion whereas a positive trend (+1.3 +/- 0.3 Tg yr(-1)) is found by the process model. Although processed-based models have their own caveats and may not take into account all processes, the positive trend found by the B-U approach is considered more likely because it is a robust feature of the process-based model, consistent with analysed precipitations and the satellite-derived extent of inundated areas. On the contrary, the surface-data based inversions lack constraints for South America. This result suggests the need for a re-interpretation of the large increase found in anthropogenic methane inventories after 2000.