The sensitivity of Pt L-edge XANES to local geometric and electronic structure in various Pt(n) clusters is investigated using the ab initio self-consistent FEFF8 code. Calculations based on FEFF8 are found to be in good agreement with experiment. For pure Pt clusters the XANES can distinguish between 2- and 3-dimensional clusters. Self-consistency is important in determining the variation of XANES with cluster size. The effect of a support is also studied. In Pt-Cl(x) clusters the presence of a Cl-Pt bond leads to a "hybridization peak," i.e., a peak in the Cl d-density of states (d-DOS) mixed with Pt d-states. For Pt-H clusters hydrogen addition is well correlated with the growth of a broad shoulder on the white line. This change is attributed largely to AXAFS, i.e., to a corresponding change in the atomic background absorption.