The phosphorylated epidermal growth factor receptor (EGFR) initiates intracellular signaling processes that regulate cell growth, survival, and migration, and disregulated EGFR-mediated signaling occurs in many cancers. While the processes that lead to EGFR activation and phosphorylation have been studied in detail, quantitative aspects of the spatiotemporal regulation of EGFR by protein tyrosines phosphatases (PTPs) are not well understood. To begin to address this, we developed a new compartmentalized mechanistic model of EGFR phosphorylation dynamics and used it to interpret quantitative biochemical measurements to show that EGFR is dephosphorylated at the plasma membrane and in the cell interior with a time scale that is small compared to the time scales for EGFR internalization. By expanding our computational model and experimental data set, we went on to demonstrate that EGFR dephosphorylation at the plasma membrane surprisingly does not affect phosphorylation-dependent EGFR internalization because a separation of phospho-dependent time scales enables EGFR to enter clathrin-coated pits prior to being acted upon by PTPs. This same separation of time scales does, however, allow PTPs to control EGFR association with adapter proteins that regulate downstream signaling. Thus, our model provides new quantitative understanding of how EGFR participates in a number of simultaneous processes that compete for EGFR C-terminal phosphotyrosines. We went on to apply this new quantitative understanding of EGFR regulation by PTPs by developing predictive models to understand how such regulation might differentially impact the efficacy of antibodies and kinase inhibitors targeting EGFR. We also developed new computational models to quantitatively predict how receptor dephosphorylation kinetics as rapid as we found for EGFR might differentially control signaling initiated by receptor tyrosine kinases that dimerize in structurally distinct ways observed naturally among the family of receptor tyrosine kinases (RTKs). Ultimately, the new quantitative understanding of EGFR regulation by PTPs developed in this thesis significantly refines our understanding of the dynamics of EGFR-mediated signaling, provides a number of additional testable predictions related to fundamental aspects of EGFR signaling complex nucleation and efficacy of EGFR-targeted therapeutics, and offers a basic quantitative framework for exploring the regulation of other receptor tyrosine kinases by PTPs.