Algebraic matroids can be used to determine all the algebraic dependency relationships among a set of polynomials, without actually calculating those corresponding polynomial relationships. I'll discuss the application of algebraic matroids in three areas of model analysis: identifiability, observability, and indistinguishability. We'll see that algebraic matroids can be particularly useful in the areas of observability and indistinguishability, especially for large nonlinear models.