Stratified squamous epithelium (SSE) consists of layers of squamous epithelial cells arranged over top of a basement membrane. The outermost layers of the nasal-oral cavity, esophagus, trachea, bronchi, cervix, vagina, and skin are all SSE. SSE constantly interacts with various stimuli, including harmful stresses. In so doing, SSE becomes the origin of several human malignancies, including esophageal squamous cell carcinoma (ESCC), head-and-neck SCC (HNSCC), cutaneous (skin) SCC (CuSCC), lung SCC (LSCC), and cervical SCC (CvSCC), which are among the most common forms of human cancers. This transformation is often associated with dysregulation of the Hippo-YAP intracellular signaling pathway. In this review, we provide an overview of how Hippo-YAP signaling drives SCC onset and development and discuss how this knowledge might lead to new therapeutic avenues for these insidious cancers.