Methodological advances in seismic tomography are often driven by the quality of data sets. The dense and homogeneous spatial coverage of the AlpArray seismic network, including hundreds of permanent and temporary broadband stations, has motivated a series of methodological develop- ments of ambient-noise-based tomography of the lithosphere across the entire Alps-Apennines re- gions, which have been published and are reviewed here. To take full advantage of the ocean-bottom seismometers (OBS) in the Ligurian-Provence basin, reconstructed Rayleigh wave signals between OBS have been improved by second-order correlations with onland stations. A Bayesian or fully trans- dimensional formalism has been introduced in both steps of isotropic ambient noise tomography. The three-dimensional S-wave velocity models have been further improved by wave-equation based inversions accounting for the physics of seismic wave propagation, including elastic–acoustic cou- pling at the sea bottom. A beamforming approach has been developed to avoid systematic errors in the measurement of azimuthal anisotropy from seismic noise. Probabilistic inversions for depth vari- ations of azimuthal and radial anisotropy have provided robust estimates of anisotropic parameters in the crust and upper mantle that differ significantly from earlier surface-wave tomography studies. These methodological improvements have taken the full benefit of the quality of available seismic data to significantly improve knowledge of the seismic structure of the crust and shallow mantle beneath the Alps-Apennines system. Our findings include detailed mapping of strong and abrupt Moho depth changes under the Western Alps, contrasting orientations of fast velocity directions between the upper and lower Alpine crust, and the absence of significant radial anisotropy everywhere in the European crust and shallow upper mantle, except in the Apenninic lower crust. These methods can be applied to similar dense arrays with equivalent potential benefits.