The YAP/TAZ family of transcriptional co-activators drives cell proliferation in epithelial tissues and cancers. Yet, how YAP and TAZ are physiologically regulated remains unclear. Here we review recent reports that YAP and TAZ act primarily as sensors of epithelial cell polarity, being inhibited when cells differentiate an apical membrane domain, and being activated when cells contact the extracellular matrix via their basal membrane domain. Apical signalling occurs via the canonical Crumbs/CRB-Hippo/MST-Warts/LATS kinase cascade to phosphorylate and inhibit YAP/TAZ. Basal signalling occurs via Integrins and Src family kinases to phosphorylate and activate YAP/TAZ. Thus, YAP/TAZ is localised to the nucleus in basal stem/progenitor cells and cytoplasm in differentiated squamous cells or columnar cells. In addition, other signals such as mechanical forces, tissue damage and possibly receptor tyrosine kinases (RTKs) can influence MST-LATS or Src family kinase activity to modulate YAP/TAZ activity.