We first describe the mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a queryable description of global dynamics of a network over its entire parameter space. We also describe a connection to Boolean network models that allows us to view DSGRN as a platform for bifurcation theory of Boolean maps. Finally, we compare DSGRN to RACIPE, an approach based on sampling parameters for ODE models.  We discuss several applications to systems biology as well as design of robust networks in synthetic biology.