The experimental technique of vibrational spectroscopy and the role that it has played in elucidating the structure and dynamics of liquid water in thermal equilibrium was investigated. Considering first the Raman line shapes, theoretical analysis indicates that the shoulder on the blue side is due to HOD molecules lacking an H-bond to the H/D atom for HDO:D2O/HDO:H 2O, respectively. The spectral diffusion observables provide quite direct information about the frequency-frequency time-correlation function. Integrated three-pulse echo-peak shift experiments show that the correlation function has an initial inertial time decay within 50 fs, a recurrence indicative of an underdamped oscillation at about 180 fs, and a long-time decay with a time constant of about 1.4 ps. As in the case of liquid water, the exquisite sensitivity of OH stretch vibrational frequencies to local environments, coupled with the excellent time and frequency resolution of modern ultrafast vibrational spectroscopy, make this an excellent technique for unraveling complicated structural and dynamical issues.