Molecular dynamics (MD) has been revealed as a powerful tool to investigate the structure and dynamics of hydrogen bonded liquids. This paper reviews recent works in which MD simulations have been used to study the influence of hydrogen bonding on different dynamic properties of liquid water and alcohols. The analysed properties include intermolecular vibrations, self-diffusion coefficients and reorientational correlation times. Finally, we present a MD study of the translational and reorientational dynamics of supercooled water at pressures up to 400 MPa. The influence of hydrogen bonding on the anomalous behaviour of the dynamic properties of liquid water at high pressures and low temperatures is discussed.