Efficient operation of mooring systems is of paramount importance to reduce floating offshore wind (FOW) energy costs. MooringSense is an R&D project which explores digitization to enable the implementation of more efficient integrity management strategies (IMS) for FOW mooring systems. In this work, the MooringSense concept is presented. It includes the development of several enablers such as a mooring system digital twin, a smart motion sensor, a structural health monitoring (SHM) system and control strategies at the individual turbine and farm levels. The core of the digital twin (DT) is a high-fidelity fully coupled numerical model which integrates simulation tools to allow predictive operation and maintenance (O&M). Relevant parameters of the coupled model are updated as physical properties evolve due to damages or degradation. The DT assimilates information coming from the physical asset and environmental sensors. Besides, a smart motion sensor provides feedback of the attitude, position, and velocity of the floater to allow the computation of virtual loads in the mooring lines, the detection of damages by the SHM system and the implementation of closed-loop control strategies. Finally, the IMS takes advantage of the mooring system updated condition information to optimize O&M, reduce costs and increase energy production.