Extended X-ray Absorption Fine Structure (EXAFS) data has been analyzed for a series of polyoxometalates (POMs) of the type [M_yO_z]^n- (isopolymetalates) and [X_xM_yO_z]^n- (heteropolymetalates) using spherical wave methods with ab initio phase shifts and backscattering factors. The raw X-ray absorption spectra were acquired mostly in the solid state at low temperature (80K) but also in some cases in solution at room temperature. The EXAFS data so derived is rich in detail about the M-O bonds (M-(η¹-O) at 1.63-1.79Å, M-(η²-O) at 1.87-1.99Å and M-(η⁴-O or η⁶-O) at 2.16-2.39Å) and also the non-bonded M...M relationships (3.0-6.0Å) which arise from pairs of edge or corner sharing distorted MO₆ octahedra and define the whole cluster geometry. Analysis of the Mo K-, Nb K-, V K- and W L_m-edge EXAFS of the hexametalates [Mo₆O₁₉]^2-, [Nb_xW_6-xO₁₉]^(x+2)- (x=6,2-4) and [V₂W₄O₁₉]^4- enables a complete structural characterisation with both the short (3.22-3.34Å) and long (4.63-4.78Å) M...M distances being accessible. The M-(η²-O)-M bond angles were determined as 113° for [Mo₆O₁₉]^2- and 112° for [HNb₆O₁₉]^7- by allowing multiple scattering for these units. Examination of the Mo K-edge solution EXAFS of [(C₄H₉)₄N]₂Mo₆O₁₉, [(C₄H₉)₄N]₃PMo₁₂O₄₀ (both in CH₃CN) and Na₃TeMo₆O₂₄.nH₂O (in water) indicates very little difference between the solid and solution structures. In general the EXAFS-derived distances compare favourably with single crystal X-ray diffraction (XRD) data, where available, suggesting that the technique could be useful in studying POMs which are important as soluble metal oxide-like analogues.