Though it is not necessarily the view taken by those who design them, modern computers are deterministic nonlinear dynamical systems, and it is both interesting and useful to treat them as such. In this talk, I will describe a nonlinear dynamics-based framework for modeling computer systems. Using this framework, together with a custom measurement infrastructure, we have found strong indications of low-dimensional dynamics in the performance of a simple program running on a popular Intel microprocessor---including the first experimental evidence of chaotic dynamics in real computer hardware. These dynamics change completely when we run the same program on a different Intel microprocessor, or when we change that program slightly. Rich models that capture these effects can be used, in some cases, to predict memory and processor loads more effectively than traditional methods. All of this raises important issues about computer analysis and design. These engineered systems have grown so complex as to defy the analysis tools that are typically used by their designers: tools that assume linearity and stochasticity, and essentially ignore dynamics. The ideas and methods developed by the nonlinear dynamics community are a much better way to study, understand, and (ultimately) design modern computer systems.