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Context. The chemical composition of the Sun is a fundamental yardstick in astronomy, relative to which essentially all cosmic objects are referenced. As such, having accurate knowledge of the solar elemental abundances is crucial for an extremely broad range of topics. Aims. We reassess the solar abundances of all 83 long-lived elements, using highly realistic solar modelling and state-of-the-art spectroscopic analysis techniques coupled with the best available atomic data and observations. Methods. The basis for our solar spectroscopic analysis is a three-dimensional (3D) radiative-hydrodynamical model of the solar surface convection and atmosphere, which reproduces the full arsenal of key observational diagnostics. New complete and comprehensive 3D spectral line formation calculations taking into account of departures from local thermodynamic equilibrium (non-LTE) are presented for Na, Mg, K, Ca, and Fe using comprehensive model atoms with reliable radiative and collisional data. Our newly derived abundances for C, N, and O are based on a 3D non-LTE analysis of permitted and forbidden atomic lines as well as 3D LTE calculations for a total of 879 molecular transitions of CH, C2, CO, NH, CN, and OH. Previous 3D-based calculations for another 50 elements are re-evaluated based on updated atomic data, a stringent selection of lines, improved consideration of blends, and new non-LTE calculations available in the literature. For elements where spectroscopic determinations of the quiet Sun are not possible, the recommended solar abundances are revisited based on complementary methods, including helioseismology (He), solar wind data from the Genesis sample return mission (noble gases), sunspot observations (four elements), and measurements of the most primitive meteorites (15 elements). Results. Our new improved analysis confirms the relatively low solar abundances of C, N, and O obtained in our previous 3D-based studies: log ϵC = 8.46 ± 0.04, log ϵN = 7.83 ± 0.07, and log ϵO = 8.69 ± 0.04. Excellent agreement between all available atomic and molecular indicators is achieved for C and O, but for N the atomic lines imply a lower abundance than for the molecular transitions for unknown reasons. The revised solar abundances for the other elements also typically agree well with our previously recommended values, with only Li, F, Ne, Mg, Cl, Kr, Rb, Rh, Ba, W, Ir, and Pb differing by more than 0.05 dex. The here-advocated present-day photospheric metal mass fraction is only slightly higher than our previous value, mainly due to the revised Ne abundance from Genesis solar wind measurements: Xsurface = 0.7438 ± 0.0054, Ysurface = 0.2423 ± 0.0054, Zsurface = 0.0139 ± 0.0006, and Zsurface/Xsurface = 0.0187 ± 0.0009. Overall, the solar abundances agree well with those of CI chondritic meteorites, but we identify a correlation with condensation temperature such that moderately volatile elements are enhanced by ≈0.04 dex in the CI chondrites and refractory elements possibly depleted by ≈0.02 dex, conflicting with conventional wisdom of the past half-century. Instead, the solar chemical composition more closely resembles that of the fine-grained matrix of CM chondrites with the expected exception of the highly volatile elements. Conclusions. Updated present-day solar photospheric and proto-solar abundances are presented for 83 elements, including for all long-lived isotopes. The so-called solar modelling problem – a persistent discrepancy between helioseismology and solar interior models constructed with a low solar metallicity similar to that advocated here – remains intact with our revised solar abundances, suggesting shortcomings with the computed opacities and/or treatment of mixing below the convection zone in existing standard solar models. The uncovered trend between the solar and CI chondritic abundances with condensation temperature is not yet understood but is likely imprinted by planet formation, especially since a similar trend of opposite sign is observed between the Sun and solar twins.