Rare-earth metal germanides with the general formula RE4Ge2 (RE = La, Ce, Pr, Nd, Sm) have been synthesized using the In-flux technique. Their structures have been established from single-crystal and powder X-ray diffraction, and the structural elucidation has been aided by electron diffraction. These compounds represent superstructures of the alpha-ThSi2 structure type through the long- and/or short-range vacancy ordering. RE4Ge7 (RE = Pr, Nd, Sm) appear to be commensurately modulated 4-fold superstructure of REGe2-x (x = 1/4), while coexistence of commensurate and incommensurate modulation is revealed in the La- and Ce-analogues. These results shed more light on the structural evolution of the REGe2-x phases as function of the vacancy concentration and nature of the rare-earth metal. Measurements of the magnetic susceptibilities on well-characterized single-crystals show ferromagnetic, antiferromagnetic, and even spin-glass-like behaviors. Mean-field theory is used to evaluate the correlations between structural and magnetic property data. Measurements on the electrical resistivities and the heat capacities are also presented and discussed.