In this talk, two synchronization phenomena of importance for the integrity and fatigue of offshore structures will be discussed, namely the VortexInduced Vibrations (VIV) and the IceInduced Vibrations (IIV) of offshore structures. The former takes place when a flexible riser is subject to marine currents, whereas the latter occurs when a flexible offshore structure, such as a channel marker or a wind turbine, is subject to drifting level ice. The mechanism of VIV is relatively well understood. It is known that the vortices shed when a cylindrical structure is subject to a timeinvariant current can be synchronized by the vibrating structure both temporarily and spatially. We will shortly revisit the VIV phenomenon with the main aim to underline its generic dynamical properties for comparison with those of the IIV. Some new findings on the VIV will also be discussed in relation to formulation of the wakeoscillator models with a nonlinear coupling.