The conjunctiva can be damaged by numerous diseases with scarring, loss of tissue and dysfunction. Depending on extent of damage, restoration of function may require a conjunctival graft. A wide variety of biological and synthetic substrates have been tested in the search for optimal conditions for ex vivo culture of conjunctival epithelial cells as a route toward tissue grafts. Each substrate has specific advantages but also disadvantages related to their unique physical and biological characteristics, and identification and development of an improved substrate remains a priority. To achieve the goal of mimicking and restoring a biological material, requires information from the material. Specifically, extracellular matrix (ECM) derived from conjunctival tissue. Knowledge of the composition and structure of native ECM and identifying contributions of individual components to its function would enable using or mimicking those components to develop improved biological substrates. ECM is comprised of two components: basement membrane secreted predominantly by epithelial cells containing laminins and type IV collagens, which directly support epithelial and goblet cell adhesion differentiation and growth and, interstitial matrix secreted by fibroblasts in lamina propria, which provides mechanical and structural support. This review presents current knowledge on anatomy, composition of conjunctival ECM and related conjunctival disorders. Requirements of potential substrates for conjunctival tissue engineering and transplantation are discussed. Biological and synthetic substrates and their components are described in an accompanying review.