Gastrulation and neurulation are successive morphogenetic processes that play key roles in shaping the basic embryonic body plan. Importantly, they operate through common cellular and molecular mechanisms to set up the three spatially organized germ layers and to close the neural tube. During gastrulation and neurulation, convergent extension movements driven by cell intercalation and oriented cell division generate major forces to narrow the germ layers along the mediolateral axis and elongate the embryo in the anteroposterior direction. Apical constriction also makes an important contribution to promote the formation of the blastopore and the bending of the neural plate. Planar cell polarity proteins are major regulators of asymmetric cell behaviors and critically involved in a wide variety of developmental processes, from gastrulation and neurulation to organogenesis. Mutations of planar cell polarity genes can lead to general defects in the morphogenesis of different organs and the coexistence of distinct congenital diseases, such as spina bifida, hearing deficits, kidney diseases, and limb elongation defects. This review outlines our current understanding of non-canonical Wnt signaling, commonly known as Wnt/planar cell polarity signaling, in regulating morphogenetic movements of gastrulation and neural tube closure during development and disease. It also attempts to identify unanswered questions that deserve further investigations.