DESY activities on 1.3 GHz tesla shape single cell and nine-cell large grain (LG) resonators are presented; results of the past five years are covered. The R&D program explores the potential for production of elliptical superconducting cavities. The main efforts have been devoted to material investigation, development of LG disk production, cavity fabrication from this material, and a search for appropriate treatment. More than 250 LG disks are manufactured; several single cell and 11 nine-cell resonators are produced and rf tested after buffered chemical polishing and after additional electropolishing. A maximum accelerating gradient of approximately 45 MV/m for this type of cavity was achieved in two resonators. Two of the LG cavities have been installed and are currently being used in the FLASH accelerator operation. Assembly of a cryomodule, consisting of LG cavities only, is in the works. Perspectives of the LG cavity application are discussed.