YAP (Yes-associated protein) is a potent oncogene and a major effector of the mammalian Hippo tumor suppressor pathway. In this review, our emphasis is on the structural basis of how YAP recognizes its various cellular partners. In particular, we discuss the role of LATS kinase and AMOTL1 junction protein, two key cellular partners of YAP that bind to its WW domain, in mediating cytoplasmic localization of YAP and thereby playing a key role in the regulation of its transcriptional activity. Importantly, the crystal structure of an amino-terminal domain of YAP in complex with the carboxy-terminal domain of TEAD transcription factor was only recently solved at atomic resolution, while the structure of WW domain of YAP in complex with a peptide containing the PPxY motif has been available for more than a decade. We discuss how such structural information may be exploited for the rational development of novel anti-cancer therapeutics harboring greater efficacy coupled with low toxicity. We also embark on a brief discussion of how recent in silico studies led to identification of the cardiac glycoside digitoxin as a potential modulator of WW domain-ligand interactions. Conversely, dobutamine was identified in a screen of known drugs as a compound that promotes cytoplasmic localization of YAP, thereby resulting in growth suppressing activity. Finally, we discuss how a recent study on the dynamics of WW domain folding on a biologically critical time scale may provide a tool to generate repertoires of WW domain variants for regulation of the Hippo pathway toward desired, non-oncogenic outputs.