The S-phase Kinase-Associated Protein 1 (SKP1) is a core component of the SKP1, Cullin 1, F-box protein (SCF) complex, an E3 ubiquitin ligase that serves to poly-ubiquitinate a vast array of protein targets as a signal for their proteasomal degradation, thereby playing a critical role in the regulation of downstream biological processes. Many of the proteins regulated by SKP1 and the SCF complex normally function within pathways that are essential for maintaining genome stability, including DNA damage repair, apoptotic signaling, and centrosome dynamics. Accordingly, aberrant SKP1 and SCF complex expression and function is expected to disrupt these essential pathways, which may have pathological implications in diseases like cancer. In this review, we summarize the central role SKP1 plays in regulating essential cellular processes; we describe functional models in which SKP1 expression is altered and the corresponding impacts on genome stability; and we discuss the prevalence of SKP1 somatic copy number alterations, mutations, and altered protein expression across different cancer types, to identify a potential link between SKP1 and SCF complex dysfunction to chromosome/genome instability and cancer pathogenesis. Ultimately, understanding the role of SKP1 in driving chromosome instability will expand upon our rudimentary understanding of the key events required for genome/chromosome stability that may aid in our understanding of cancer pathogenesis, which will be critical for future studies to establish whether SKP1 may be useful as prognostic indicator or as a therapeutic target.