We study the structure of water through molecular dynamics, specifically the compression/expansion of the hydrogen-bond (H-bond) network, with temperature and pressure, and in salt solutions of alkali chlorides and sodium halides, and relate the observed local spatial perturbations with the tetrahedrality and the average number and lifetime of water H-bonds. The effect of transient H-bonds and transient broken H-bonds on H-bond lifetimes is further investigated, and results are compared with depolarized Rayleigh scattering lifetimes for neat water. A significant electrostriction is observed in the first hydration shell of Li+ and F-, while larger ions cause a small expansion of the H-bond network of water instead. However, both alkali cations and halide anions induce a minor contraction of the H-bond network in the second hydration shell. Further, water in the second hydration shell of Li+, Na+, and K+ is less tetrahedral than neat water, resembling water at high pressures, while the H-bond network in the respective hydration shell of halide anions resembles water at low temperatures. Nevertheless, neither ion induced H-bond contraction nor expansion can be exactly mapped onto P or T effects on the local structure of water. Even though the average number and lifetime of H-bonds in the ionic hydration shells of most ions are not very different from those found in neat water, Li+ and F- significantly increase the lifetime of water donor and acceptor H-bonds, respectively, in the first hydration shell. The non-monotonic increase of cation and anion mobility, with ionic size, observed experimentally, is interpreted in terms of the water local tetrahedrality around cations and anions.