This paper presents recent advances in the use of molecular simulations and extended X-ray absorption fine structure (EXAFS) spectroscopy, which enable us to understand solvated ions in solution. We report and discuss the EXAFS spectra and related properties governing solvation processes of different ions in water and methanol. Molecular dynamics (MD) trajectories are coupled to electron scattering simulations to generate the MD-EXAFS spectra, which are found to be in very good agreement with the corresponding experimental measurements. From these simulated spectra, the ion-oxygen distances for the first hydration shell are in agreement with experiment within 0.05-0.1 angstrom. The ionic species studied range from monovalent to divalent, positive and negative: K+, Ca2+, and Cl-. This work demonstrates that the combination of MD-EXAFS and the corresponding experimental measurement provides a powerful tool in the analysis of the solvation structure of aqueous ionic solutions. We also investigate the value of electronic structure analysis of small aqueous clusters as a benchmark to the empirical potentials. In a novel computational approach, we determine the Debye-Waller factors for Ca2+, K+, and Cl- in water by combining the harmonic analysis of data obtained from electronic structure calculations on finite ion-water clusters, providing excellent agreement with the experimental values, and discuss how they compare with results from a harmonic classical statistical mechanical analysis of an empirical potential.