Modern systems biology and synthetic bioengineering face two major challenges in relating properties of the genetic components of a natural or engineered system to its integrated behavior. The first is the fundamental unsolved problem of relating the digital representation of the genotype to the analog representation of the parameters for the molecular components. For example, knowing the DNA sequence does not allow one to determine the kinetic parameters of an enzyme. The second is the fundamental unsolved problem of relating the parameters of the components and the environment to the phenotype of the global system. For example, knowing the parameters does not tell one how many qualitatively distinct phenotypes are in the organism's repertoire or the relative fitness of the phenotypes in different environments. These also are challenges for biomedical engineers as they attempt to develop therapeutic strategies to treat pathology or to redirect normal cellular functions for biotechnological purposes. In this article, the second of these fundamental challenges will be addressed, and the notion of a "system design space" for relating the parameter space of components to the phenotype space of bioengineering systems will be focused upon. First, the concept of a system design space will be motivated by introducing one of its key components from an intuitive perspective. Second, a simple linear example will be used to illustrate a generic method for constructing the design space in which qualitatively distinct phenotypes can be identified and counted, their fitness analyzed and compared, and their tolerance to change measured. Third, two examples of nonlinear systems from different areas of biomedical engineering will be presented. Finally, after giving reference to a few other applications that have made use of the system design space approach to reveal important design principles, some concluding remarks concerning challenges and opportunities for further development will be made.