Experiments have demonstrated that changing the rate at which the ribosome translates a codon position in an mRNA molecules open reading frame can alter the behavior of the newly synthesized protein. That is, codon translation rates can govern nascent proteome behavior. We emphasize that this phenomenon is a manifestation of the nonequilibrium nature of cotranslational processes, and as such, there exist theoretical tools that offer a potential means to quantitatively predict the influence of codon translation rates on the broad spectrum of nascent protein behaviors including cotranslational folding, aggregation, and translocation. We provide a review of the experimental evidence for the impact that codon translation rates can have, followed by a discussion of theoretical methods that can describe this phenomenon. The development and application of these tools are likely to provide fundamental insights into protein maturation and homeostasis, codon usage bias in organisms, the origins of translation related diseases, and new rational design methods for biotechnology and biopharmaceutical applications.