Electronic, optical, and thermoelectric properties of germanium tellurides (GeTe) were investigated through a series of first-principles calculations of band structures, absorption coefficients, and thermoelectric transport coefficients. We consider bulk GeTe to consist of cubic and rhombohedral phases, while the two-dimensional (2D) GeTe monolayers can form as a 2D puckered or buckled honeycomb crystals. All of the GeTe variants in the bulk and monolayer shapes are excellent light absorbers in a wide frequency range: (1) bulk cubic GeTe in the near-infrared regime, (2) bulk rhombohedral GeTe and puckered monolayer GeTe in the visible-light regime, and (3) buckled monolayer GeTe in the ultraviolet regime. We also found specifically that the buckled monolayer GeTe exhibits remarkable thermoelectric performance compared to the other GeTe phases due to a combination of electronic band convergence, a moderately wide band gap, and unique 2D density of states from the quantum confinement effect.