A paradigm shift is underway in which the classical materials selection approach in engineering design is being replaced by the design of material structure and processing paths on a hierarchy of length scales for specific multifunctional performance requirements. In this dissertation, the focus is on designing mesoscopic material and product topology?? geometric arrangement of solid phases and voids on length scales larger than microstructures but smaller than the characteristic dimensions of an overall product. Increasingly, manufacturing, rapid prototyping, and materials processing techniques facilitate tailoring topology with high levels of detail. Fully leveraging these capabilities requires not only computational models but also a systematic, efficient design method for exploring, refining, and evaluating product and material topology and other design parameters for targeted multifunctional performance that is robust with respect to potential manufacturing, design, and operating variations. In this dissertation, the Robust Topological Preliminary Design Exploration Method is presented for designing complex multi-scale products and materials by topologically and parametrically tailoring them for multifunctional performance that is superior to that of standard designs and less sensitive to variations. A comprehensive robust design method is established for topology design applications. It includes computational techniques, guidelines, and a multiobjective decision formulation for evaluating and minimizing the impact of topological and parametric variation on the performance of a preliminary topological design. A method is also established for multifunctional topology design, including thermal topology design techniques and multi-stage, distributed design methods for designing preliminary topologies with built-in flexibility for subsequent modification for enhanced performance in secondary functional domains. Key aspects of the approach are demonstrated by designing linear cellular alloys??ered metallic cellular materials with extended prismatic cells?? three applications. Heat exchangers are designed with increased heat dissipation and structural load bearing capabilities relative to conventional heat sinks for microprocessor applications. Cellular materials are designed with structural properties that are robust to dimensional and topological imperfections such as missing cell walls. Finally, combustor liners are designed to increase operating temperatures and efficiencies and reduce harmful emissions for next-generation turbine engines via active cooling and load bearing within topologically and parametrically customized cellular materials.