Methane emission estimates are presented from four different atmospheric inversion frameworks for the period 2005 to 2018. These flux estimates were prepared in the framework of the H2020 project, VERIFY. Included are the gridded fluxes at monthly temporal resolution and either at 0.5x0.5 or 1.0x1.0 degrees spatial resolution depending on the inversion. Although two of the inversions present global gridded fluxes, the target region for all inversions is geographical Europe. Also included are country total emissions for all EU27 + UK countries at monthly resolution. All inversions use the same prior flux estimate, which includes empirical and process-based model estimates for all anthropogenic sources as well as for natural sources from geological manifestations, lakes, peatland and mineral soils. The files are named after the inversion frameworks (see below). The datasets are the following: Carbon-Tracker Europe CH4 (in the filenames this is abbreviated as CTE): a Bayesian inversion framework based on the Eulerian atmospheric transport model, TM5, and using an Ensemble Kalman Filter algorithm. The gridded fluxes are at 1.0x1.0 degrees resolution and in units of kgCH4/m2/month. The gridded flux file contains variables for the prior and posterior fluxes from soils (bio_flux_prior and bio_flux_opt), and from anthropogenic sources (anth_flux_prior and anth_flux_opt) and their prior and posterior uncertainties (bio_flux_prior_std, bio_flux_opt_std, anth_flux_prior_std and anth_flux_opt_std) calculated as the standard deviation of the ensemble members. Also included are fluxes from wildfires (fire_flux_imp), ocean (ocn_flux_imp), geological manifestations (geol_flux_imp), and the total prior and posterior flux (total_flux_pri and total_flux_opt) and their uncertainties (total_flux_pri_std and total_flux_opt_std). FLEXINVERT: a Bayesian inversion framework based on the Lagrangian atmospheric transport model, FLEXPART. The gridded fluxes are at 0.5x0.5 degrees resolution and are in units of kgCH4/m2/y. The gridded flux file contains variables for the prior and posterior total flux (FCH4_TOT_pri and FCH4_TOT_post), the posterior flux after applying an inequality constraint (FCH4_TOT_post_constrained), and the prior and posterior flux uncertainties (FCH4_TOT_epri and FCH4_TOT_epos). FLEXPART-ExKF (in the filenames this is abbreviated as FLEXKF): a Bayesian inversion framework based on the Lagrangian atmospheric transport model, FLEXPART, using an Extended Kalman Filter algorithm. The gridded fluxes are at 0.5x0.5 degrees resolution and are in units of kgCH4/m2/h. The gridded flux file contains variables for the prior and posterior total flux (FCH4_PRIOR and FCH4_POST), and the prior and posterior flux uncertainties (FCH4_PRIOR_UNCERT and FCH4_POST_UNCERT). TM5-4DVAR: a Bayesian inversion framework based on the Eulerian atmospheric transport model, TM5, and using a 4D-var algorithm. The gridded fluxes are at 1.0x1.0 degrees resolution and in units of kgCH4/m2/h. The gridded flux file contains variables for the prior and posterior total flux (FCH4_PRIOR and FCH4_POST).