Earth composition models rely on three types of information: petrological sampling, geophysical sounding, and cosmochemical constraints. The relative input of a given category of information changes with the depth of the considered Earth's layer. The constraints brought by the petrological approach are dominant for the upperparts of the Mantle, whereas geophysical constraints play a crucial role for estimating deep Earth (lower mantle and core) composition. Since a direct sampling of the deep Earth is not possible, chemical constraints are mainly brought by the composition of primitive chondrites. In the more general approach, chondritic refractory lithophile elements (RLE) ratios are used to infer their content in the mantle. In addition, the family of "E-Earth models" uses not only chondritic RLE ratios, but also the bulk composition of a particular family of chondrites: enstatite (EH, EL) chondrites. These chondrites are the closest to the Earth in terms of isotopic composition as well as redox state and can be used to infer the composition of the deep Earth following a mass balance approach. In this paper, we first review the main characteristics of E-Chondrites in relation to the isotopic and redox characteristics of the Earth. We then present the main steps of the determination of the Earth composition based on a generic model of E-chondrites, and we then expand our previous results to the content of some minor and major trace elements in the deep mantle. The general characteristics of E-Earth compositions and their consequences for Earth differentiation and dynamics are discussed, and paths for further improvements of the model are presented.