The cornea is an avascular, transparent ocular tissue that serves as a refractive and protective structure for the eye. Over 90% of the cornea is composed of a collagenous-rich extracellular matrix within the stroma with the other 10% composed by the corneal epithelium and endothelium layers and their corresponding supporting collagen layers (e.g., Bowman's and Descemet's membranes) at the anterior and posterior cornea, respectively. Due to its prominent role in corneal structure, tissue engineering approaches to model the human cornea in vitro have focused heavily on the cellular and functional properties of the corneal stroma. In this review, we discuss model development in the context of culture dimensionality (e.g., 2-dimensional versus 3-dimensional) and expand on the optical, biomechanical, and cellular functions promoted by the culture microenvironment. We describe current methods to model the human cornea with focus on organotypic approaches, compressed collagen, bioprinting, and self-assembled stromal models. We also expand on co-culture applications with the inclusion of relevant corneal cell types, such as epithelial, stromal keratocyte or fibroblast, endothelial, and neuronal cells. Further advancements in corneal tissue model development will markedly improve our current understanding of corneal wound healing and regeneration.