Gene network dynamics and neural network dynamics face similar challenges of high dimensionality of both phase space and parameter space, and a lack of reliable experimental data to infer parameters. We first describe the mathematical foundation of DSGRN (Dynamic Signatures Generated by Regulatory Networks), an approach that provides a combinatorial description of global dynamics of a network over its parameter space. Finite description allows comparison of parameterized dynamics between hundreds of networks to discard networks that are not compatible with experimental data. We also describe a close connection of DSGRN to Boolean network models that allows us to view DSGRN as a connection between parameterized continuous time dynamics and discrete dynamics of Boolean modets. If time allows, we discuss several applications of this methodology to systems biology.