Plant tissues commonly undergo morphogenesis within a single tissue layer or between associated cells of the same tissue type such as vascular cells. Tissue morphogenesis may rely on an underlying tissue polarity marked by coordinated unidirectional asymmetric localisation of molecules to ends of cells. When observed in the plane of the tissue layer this is referred to as planar polarity and planar morphogenesis. However, planar morphogenesis can also involve multidirectional or differential growth of cells relying on cell-cell communication. Here, we review recent progress towards an understanding of hormonal coordination and molecular mechanisms underlying planar and tissue polarity as well as planar morphogenesis. Furthermore, we discuss the role of physical forces in planar morphogenesis and the contribution of tissue polarity to plant organ shape.