Understanding the structures of medium-sized protonated water clusters [H+(H2O)(n)] has made a significant advancement recently thanks to the development of new experimental techniques and high-level computational methods. A combination of vibrational predissociation spectroscopy and ab initio calculations was shown to be effective in elucidating the structures of the clusters as a function of their temperature and size. The combined study revealed several intriguing features ( such as symmetric hydrogen bonds) that could not be found for neutral water clusters. However, similar to its neutral counterpart, the number of stable isomers increases exponentially with cluster size ( n), making direct structural identification of medium-sized clusters difficult. Despite the difficulties, both experimental and computational results indicated a smooth change in hydrogen-bond topology from tree-like, single-ring, multiple-ring to polyhedron-like structures ( and their mixtures) as n increases from 5 to 28. The excess proton can be symmetrically hydrated at n = 6 - 8. Five-membered ring isomers can form at n = 7 and 8 as the low-lying minima. Only a single feature ( similar to 3695 cm(-1)) in the free OH stretching region was observed for H+(H2O)(21) and H+(H2O)(28), suggesting that all surface water molecules are linked in a similar 3- coordinated (double-acceptor-single-donor, (AAD)) configuration in both "magic number'' clusters. The clathrate-like structures open up at higher temperatures, as evidenced by the increased intensity of the free-OH stretching absorption band (similar to 3715 cm(-1)) of 2-coordinated (single-acceptor-single-donor, ( AD)) water molecules. Further understanding of the structures and thermal properties of these clusters is gained through the studies with Monte Carlo ( MC) and molecular dynamics simulations, ion reactivity and thermal dissociation measurements, as well as Ar tagging experiments.