The U.S. offshore wind resource potential is immense, and often in close proximity to densely-populated coastal load centers. In many U.S. coastal areas, water depths favor the deployment of floating over fixed-bottom offshore wind technology. Floating offshore wind plants have the potential to be cost-competitive with fixed-bottom installations, but because the technology has not yet been deployed at commercial scale, it is not clear when and with what configurations this potential cost parity can be achieved. This article first reviews the state of floating offshore wind technology and deployments to identify key gaps that must be addressed to bring down the overall cost of energy produced. The article then puts forth a long-term vision for a research program and design methodology that may be able to push floating wind plants toward a lower levelized cost of energy than fixed-bottom offshore wind. The method involves a fully integrated systems-engineering and techno-economic design approach to capture the complex interactions between the physics, manufacturing, installation, and operation of floating wind turbines to achieve transformational cost reductions. The approach also envisions multifidelity and uncertainty management strategies to examine the most robust and viable concepts in the design trade-space. To better focus the computational resources, engineering lessons learned from existing offshore wind systems and concept studies are used to develop a set of criteria that can be applied to prefilter candidate technology building blocks that have the greatest cost reduction potential.