We develop a general method for applying functional models to natural systems and cite recent progress in protein modeling that demonstrates the power of this approach. Functional modeling constrains the range of acceptable structural models of a system, reduces the difficulty of finding them, and improves their fidelity. However, functional models are distinctly different from the structural models that are more commonly applied in science. In particular, structural and functional models ask different questions and provide different kinds of answers. As we clarify these differences and articulate how to use these models jointly, we extend our ability to do science and gain insight into the proper use of the terms organization, order, and emergence when describing systems in nature.