Novel technologies, fabrication methods, controllers and computational methods are rapidly advancing the capabilities of soft robotics. This is creating the need for design techniques and methodologies that are suited for the multi-disciplinary nature of soft robotics. These are needed to provide a formalized and scientific approach to design. In this paper, we formalize the scientific questions driving soft robotic design; what motivates the design of soft robots, and what are the fundamental challenges when designing soft robots? We review current methods and approaches to soft robot design including bio-inspired design, computational design and human-driven design, and highlight the implications that each design methods has on the resulting soft robotic systems. To conclude, we provide an analysis of emerging methods which could assist robot design, and we present a review some of the necessary technologies that may enable these approaches.