Neural tube closure has been studied for many decades, across a range of vertebrates, as a paradigm of embryonic morphogenesis. Neurulation is of particular interest in view of the severe congenital malformations – ‘neural tube defects’ – that result when closure fails. The process of neural tube closure is complex and involves cellular events such as convergent extension, apical constriction and interkinetic nuclear migration, as well as precise molecular control via the non-canonical Wnt/planar cell polarity pathway, Shh/BMP signalling, and the transcription factors Grhl2/3, Pax3, Cdx2 and Zic2. More recently, biomechanical inputs into neural tube morphogenesis have also been identified. Here, we review these cellular, molecular and biomechanical mechanisms involved in neural tube closure, based on studies of various vertebrate species, focusing on the most recent advances in the field.