Four different density functional methods have been employed to study the molecular structures, electron affinities, and first dissociation energies of the GeFn/GeFn-(n=1-5) molecules. The three types of electron affinities reported in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first Ge-F dissociation energies D-e(Fn-1Ge-F), D-e(Fn-1Ge--F), and D-e(Fn-1Ge-F-) of the GeFn/GeFn- species are also reported. The basis set used in this work is of double-zeta plus polarization quality with additional s- and p-type diffuse functions, labeled as DZP++. Among the four density functionals used in this work, the BHLYP (which includes 50% exact exchange) method determines the molecular structures in best agreement with experiment, while other methods generally overestimated bond lengths. The theoretical Ge-F bond distances for the GeFn- (n=1-4) anions are predicted about 0.1 A longer than their corresponding neutral counterparts. No significantly bound minimum was found for the neutral GeF5 molecule, while a D-3h structure was confirmed to be a genuine minimum for ionic GeF5-. Based on the precise experimental result of EA(ad)(GeF), the adiabatic electron affinities obtained at the DZP++ BHLYP level of theory are again most reliable, with the BLYP method being next. The DZP++ BHLYP adiabatic electron affinities are 1.02, 0.85, 3.72, and 1.46 eV for GeF, GeF2, GeF3, and GeF4, respectively. The vertical detachment energy of GeF5- is predicted to be very large. The substantial value (1.46 eV) of the EA for GeF4 is especially interesting, in that the valence isoelectronic species SiF4 does not bind an electron. A number of experimental electron affinities and experimental thermochemical quantities appear to be error.