The internalization of multi-cellular tissues is a key morphogenetic process during animal development and organ formation. A good example of this is the initial stages of vertebrate central nervous system formation whereby a transient embryonic structure called the neural plate is able to undergo collective cell rearrangements within the dorsal midline. Despite the fact that defects in neural plate midline internalization may result in a series of severe clinical conditions, such as spina bifida and anencephaly, the biochemical and biomechanical details of this process remain only partially characterized. Here we review the main cellular and molecular mechanisms underlying midline cell and tissue internalization during vertebrate neural tube formation. We discuss the contribution of collective cell mechanisms including convergence and extension, as well as apical constriction facilitating midline neural plate shaping. Furthermore, we summarize recent studies that shed light on how the interplay of signaling pathways and cell biomechanics modulate neural plate internalization. In addition, we discuss how adhesion-dependent cell-cell contact appears to be a critical component during midline cell convergence and surface cell contraction via cell-cell mechanical coupling. We envision that more detailed high-resolution quantitative data at both cell and tissue levels will be required to properly model the mechanisms of vertebrate neural plate internalization with the hope of preventing human neural tube defects.