Offshore wind provides an important source of renewable energy. While wind turbines fixed to the seabed in shallow water have already been industrialized, floating wind turbines are still at an early stage of development. The cost of wind power is decreasing fast. Yet, the main challenges, especially for novel floating wind turbine concepts, are to increase reliability and reduce costs. The reliability perspective here refers to the lifecycle integrity management of the system to ensure reliability by actions during design, fabrication, installation, operation, and decommissioning. The assessment should be based on response analysis that properly accounts for the effect of different sub-systems (rotor, drivetrain, tower, support structure, and mooring) on the system behavior. Moreover, the load effects should be determined so as to be proper input to the integrity check of these sub-systems. The response analysis should serve as the basis for design and managing inspections and monitoring, with due account of inherent uncertainties. In this paper, recent developments of methods for numerical and experimental response assessment of floating wind turbines are briefly described in view of their use to demonstrate system integrity in design as well as during operation to aid inspection and monitoring. Typical features of offshore wind turbine behavior are also illustrated through some numerical case studies.