Mathematical and computational modeling have become an indispensible component of research across the sciences. Nevertheless, there are still many examples of research across the sciences where decision making processes are strongly influenced by empirical approaches rather than theory. One of the primary challenges in developing rigorous models of complex processes is capturing the nonlinear interactions of processes across multiple scales in space and time. At the same time, because such models may contain many parameters and can describe wide ranges of behaviors, new methods for parameter estimation and inference are needed as well. In this talk, I will give several examples of new multiscale models and novel applications of parameter inference methodologies in applications ranging from tumor biology to engineering. I will discuss some open problems where there are significant opportunities for future research.