A critical review about the existing theories of extended fine structure of the X-ray absorption spectra of polycrystalline and amorphous solids is given. The fine structure of the K-absorption has been calculated according to the HAYASI, SHIRAIWA and KOZLENKOV theory using different potential models for each time one representative of the simple lattice types (Cr for the bcc, CrH for the hex and Ge for the diamond lattice). In some cases the crystal potential has been approximated by the superposition of the HARTREE-FOCK potentials of the isolated atoms according to their arrangement in the crystal. A comparison of the calculated fine structure curves between each other as well as with the experiment shows that the short-range order theories reproduce the shape of the fine structure curves qualitatively and the positions of the fine structure extrema partially quantitatively. However, to be able to reproduce the experimental fine structure in all details, these theories have to be improved especially by a more detailed consideration of the interactions of the photoelectron with the neighbouring atoms and the conduction electrons.