Inferring the structure and dynamical interactions of complex biological systems is critical to understanding and controlling their behavior. I am interested in discovering mechanistic and informative models, assuming I have time-series data of important state variables and knowledge of the possible types of interactions between state variables. The problem is then selecting which interactions, or model terms, are most likely responsible for the observed dynamics. Several challenges make model selection difficult including nonlinearities and unmeasured state variables. I will discuss methods for reframing these problems so that sparse model selection is possible. I will discuss preliminary results on parameter estimation, model selection, and experimental design to characterize a spatially organized metabolism pathway in bacteria and generic chaotic systems. Parameter estimation and model selection are challenging in these cases because only some of the metabolite pools or state variables can be measured and the other variables are hidden or latent. We use a combination of data assimilations techniques and sparse optimization to perform model selection. Experimental design is enabled through sensitivity analysis of the model manifold.