Gene expression is a fundamental cellular process by which proteins are synthesized based on the information encoded in the genetic material. During this process, macromolecules such as ribosomes or RNA polymerases scan the genetic material in a sequential manner. We review several deterministic, continuous-time models for the flow of such macromolecules. These models are both easy to simulate and amenable to rigorous mathematical analysis. We demonstrate how these models can be used to predict the expression levels of genes and to study important biological phenomena such as competition for finite resources, sensitivity of gene expression to various biophysical factors, and optimization of the protein production rate.