Topology optimization (TO) is a mathematical method to find the optimal size, shape and connectivity of a domain under specified conditions, and has had many applications in engineering design. However, challenges remain in realizing TO as an effective design tool for many design situations. Uncertainty is ubiquitous in nature and has an acute impact on the design of engineered systems. This research proposes to integrate uncertainty into TO in the forms of reliability-based and robust reliability-based design, addressing the specific challenge of spatially varying material uncertainty. Additionally, topology optimized designs often possess complex geometries making it difficult to manufacture such designs using conventional methods. Additive Manufacturing (AM) is capable of handling such complexities; advances in AM allow for use of rubber-like materials, which are modeled by hyperelastic constitutive laws, to produce complex structures designed by TO. In this research, different models of hyperelastic materials are investigated and their influences on the resulting topologies illustrated. Case studies for all design problems are presented and studies performed to understand the influence of differing uncertainties and hyperelasticity on the resulting topologies.