Seismic tomography is an essential tool for the solution of a large variety of scientific and societal problems, including the exploration for natural resources, the monitoring of CO2 storage and the inference of the Earth?s dynamics and evolution. Recent progress in numerical seismology and high-performance computing has led to the development of full waveform tomography (FWT) where the complete seismic wavefield can be modelled and exploited. The results are images of the Earth?s interior with unprecedented resolution. Despite substantial advances, key problems in seismic tomography remain unsolved or highly debated. These include the 3D density structure and the intrinsic anisotropy of the Earth?s interior. Both are essential for an improved understanding of our planet?s dynamics and constitution on all scales. The principal objectives of the EWTOMO project are the development of FWT techniques to infer 3D density and anisotropy variations in the Earth in general and beneath Europe in particular. Key scientific questions to be answered are: (1) What is the 3D density and anisotropy structure beneath Europe? (2) Which functionals of seismic data are most sensitive to 3D density structure? (3) How can we combine seismic and gravity data to constrain 3D Earth structure? (4) How do density and anisotropy trade off in tomographic inversions? (5) How can we jointly invert for crust and mantle structure to avoid erroneous images of anisotropy?