Epiboly is a conserved gastrulation movement describing the thinning and spreading of a sheet or multi-layer of cells. The zebrafish embryo has emerged as a vital model system to address the cellular and molecular mechanisms that drive epiboly. In the zebrafish embryo, the blastoderm, consisting of a simple squamous epithelium (the enveloping layer) and an underlying mass of deep cells, as well as a yolk nuclear syncytium (the yolk syncytial layer) undergo epiboly to internalize the yolk cell during gastrulation. The major events during zebrafish epiboly are: expansion of the enveloping layer and the internal yolk syncytial layer, reduction and removal of the yolk membrane ahead of the advancing blastoderm margin and deep cell rearrangements between the enveloping layer and yolk syncytial layer to thin the blastoderm. Here, work addressing the cellular and molecular mechanisms as well as the sources of the mechanical forces that underlie these events is reviewed. The contribution of recent findings to the current model of epiboly as well as open questions and future prospects are also discussed.