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The paper gives a review of the achievements in the applications of marine hydrodynamics to problems in offshore and maritime engineering. In particular focus will be on numerical methods for analysis of ships and floating production systems and how the work of Professor Newman has influenced the development of computational tools for use by the industry. The paper also presents some recent applications of such numerical tools for analysis of fixed and floating production systems, seakeeping of ships with forward speed including problems related to sloshing and moonpool dynamics. The challenges for each of these applications will be discussed from a physical viewpoint and how the numerical tools are applied to solve the problems. Validation of computer tools in light of their intrinsic limitations will be discussed. Finally the paper presents some of the most important engineering challenges today with respect to modelling and simulation of loads and response of ships and floating production systems.