The dynamics of water molecules within the hydration shell surrounding a biomolecule can have a crucial influence on its biochemical function. Characterizing their properties and the extent to which they differ from those of bulk water have thus been long-standing questions. Following a tutorial approach, we review the recent advances in this field and the different approaches which have probed the dynamical perturbation experienced by water in the vicinity of proteins or DNA. We discuss the molecular factors causing this perturbation, and describe how they change with temperature. We finally present more biologically relevant cases beyond the dilute aqueous situation. A special focus is on the jump model for water reorientation and hydrogen bond rearrangement.