Tissue engineering is the construction, repair or replacement of damaged or missing tissue in humans and other animals. This engineering may take place within the animal body or as tissue constructs to be made in a bioreactor for later grafting into the animal. The minimal set of materials for this are the appropriate types of cell. Usually, however, non-living substrata are used as well. These substrata may be nothing more than materials that bulk up any voids in the damaged tissue and provide the mechanical strength that has been lost when the tissue is damaged or removed. They may serve a similar pair of functions in the bioreactor. They can do much more in terms of pattern formation. The orientations and morphology of the cells, the arrangement of intercellular material as it is laid down and the relationships between different cell types in the repairing or construct tissue are all of importance, for these should resemble the correct normal tissue as closely as possible. Most of these requirements are ones involving pattern formation. This review discusses the various ways in which tissue pattern can be engineered chiefly from a biophysical standpoint. Unpatterned cells are effectively not tissue. This engineering includes the use of topography on the substrata, chemical patterning of adhesive and other cues for the cells, mechanical force application to cause cell orientation and appropriate synthetic responses and electrical fields. The review also discusses the methods used to impart the appropriate cues to and through the materials which are often biodegradable polymers. The article gives particular attention to regions of research and practice where the involvement of the physicist or biophysicist is of importance.