The present invention relates to a biopolymer covering for a tissue surface including, for example, a dressing, a bandage, a drape such as a bandage contact lens, a composition or covering to protect tissue, a covering to prevent adhesions, to exclude bacteria, to inhibit bacterial activity, or to promote healing or growth of tissue. An example of such a composition is an amniotic membrane covering for an ocular surface. Use of a covering for a tissue surface according to the invention eliminates the need for suturing. The invention also includes devices facilitating the fastening of a membrane to a support, culture inserts, compositions, methods, and kits for making and using coverings for a tissue surface and culture inserts. Compositions according to the invention may include cells grown on a membrane or attached to a membrane, and such compositions may be used as scaffolds for tissue engineering or tissue grafts. A method of preparing and using an amniotic membrane covering for a tissue surface as a controlled release drug delivery vehicle is also disclosed.