Cells use chemistry to process complex information and make decisions. How should a stem cell differentiate? What prompts a cancer cell to enter a metastatic state? How does a cell know when to undergo apoptosis? Over the past several decades, a growing trove of biomolecular data has enabled detailed insights into the gene and protein interactions that underlie these biomolecular decisions. Still, much work remains to transform this unprecedented wealth of data into cohesive understanding and to leverage that understanding to efficiently develop novel clinical therapies. A crucial step toward these goals is the construction and analysis of predictive dynamical models, which integrate biomolecular data to generate testable and mathematically precise predictions about the effect of genetic modifications and pharmaceutical interventions. A fundamental difficulty that limits modeling in both clinical and laboratory settings is that, due to their high dimension and extreme nonlinearity, these models are computationally difficult to construct and analyze. One approach, first developed for the analysis of qualitative discrete models of biomolecular circuits, is to analyze so-called “stable motifs”, or self-sustaining patterns of activity in small subcircuits within a larger model. Collective dynamics of the entire network is inferred from the interactions between these patterns and their downstream effects. In the first part of my dissertation, I present my work on the extension of stable motifs to study oscillations in asynchronously updated Boolean networks and an application to a model of the genetic circuitry that drives the cell cycle. I also present my work on pystablemotifs, a Python library that implements efficient algorithms for the attractor identification and control in asynchronous Boolean networks. In the second part of my dissertation, I present my generalizations of these concepts from discrete dynamics to the study of ODEs and show the utility of this approach in controlling and parameterizing ODEs.