SRC homology 2 domain-containing phosphatase 2 (SHP2) is a ubiquitously expressed cytosolic protein tyrosine phosphatase. Downstream of epidermal growth factor receptor (EGFR) and other receptors, SHP2 is activated by binding to phosphotyrosine-containing receptors and adapter proteins, is required for complete extracellular regulated kinase 1/2 (ERK) pathway activity, which promotes cellular proliferation and survival, and regulates other signaling processes. In this thesis, we explored the signaling functions of SHP2 in lung and brain cancer cell systems with or without clinically relevant mutations that render EGFR constitutively active and developed computational models of EGFR-mediated SHP2 activation. In non-small cell lung cancer cells, SHP2 promoted ERK-dependent resistance to EGFR inhibition, but in cells with EGFR kinase-activating mutations this SHP2 functional role was impaired through sequestration of biochemically active SHP2 with internalization-impaired EGFR mutants. In glioblastoma multiforme cells, SHP2 simultaneously promoted ERK activity and antagonized STAT3 phosphorylation such that SHP2 drove proliferation while also promoting sensitivity to EGFR and c-MET co-inhibition. These SHP2 functions were perturbed by sufficiently high expression of the EGFR variant III mutant. Furthermore, SHP2 was found to regulate EGFRvIII and c-MET phosphorylation and control hypoxia-inducible factor expression in a way that may regulate tumorigenesis. We next developed computational models and associated quantitative experimental data sets to gain quantitative understanding of the regulation of protein complexes containing SHP2 and GRB2-associated binder 1 (GAB1), the primary phosphorylated adapter with which SHP2 associates following EGFR activation. Our analysis revealed that in some cell settings EGFR activity is amplified by intermediary SRC family kinases (SFKs) which drive GAB1 phosphorylation and enable GAB1-SHP2 complexes to persist in the cytosol distal from EGFR. A reaction-diffusion model further predicted that EGFR-initiated GAB1-SHP2 complexes persist over the entire cell length scale, which could permit membrane-localized EGFR to regulate signaling events through SHP2 at subcellular locations where EGFR itself is not present. Overall, these results motivate the continued search for specific SHP2 inhibitors, while providing a contextual basis for predicting when such interventions may be particularly effective, and establish a quantitative framework for understanding EGFR's ability to activate SHP2 and how this might be perturbed in different pathological contexts.