The problem solved in the REM3D project can be described as a system of equations, or an inverse problem, to find models of seismic sources and Earth structure that reproduce most accurately the measured data. In global seismology, three classical concepts are typically used in the interpretation of recorded seismograms. The broadband body-wave arrivals (T 1–10 s) in the first few tens of minutes of a seismogram can be analyzed using ray-theoretical methods akin to geometrical optics. The large-amplitude, dispersed surface waves (T 25–250 s) arriving in the first few minutes to hours of a seismogram are analyzed using characteristics that describe a wave packet such as group and phase velocity. The third concept is that of free oscillations of the whole Earth that manifest as resonance peaks in the spectra of very long seismograms. The spectral peaks at the longest periods (T ≥ 250 s) are fingerprints of various types of standing waves in the whole Earth caused by a major earthquake. Recently, we pioneered full-spectrum tomography that employs all aforementioned data types along with complete seismic waveforms, while accounting for various theoretical complexities like anisotropy and attenuation. Additional catalogs from related efforts are available on the data webpage.