In this paper, we present several applied as well as fundamental research problems related to the future needs of the offshore engineering. The paper starts out with a detailed discussion of the current uncertainties and constraints. Then, specific research issues on environmental input conditions, on the role of computational fluid dynamics, and on damping and dynamic response are presented. It is suggested that an appreciation of the input parameters, acquisition of extensive data to properly characterize the ocean environment, development of new methods and tools to acquire relevant data, extensive use of the computational methods, basic/applied research on the dynamic response and damping of structures, use of new materials, science-and-technology transfer from sister disciplines (e.g., aerospace industry, keeping in mind the complexities brought about by the presence of the air-water interface), and other related research will significantly enhance our ability to design and build a variety of safer and economical offshore structures in deeper waters as well as over marginal fields in the next few decades. This herculean effort will require several decades of complementary experimental, numerical and analytical studies of ocean-structure interaction which will serve to elucidate the basic as well as applied fluid mechanics phenomena relevant to the offshore mechanics.